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Full text of "A critical exposition of the philosophy of Leibniz, with an appendix of leading passages"



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http://www.archive.org/details/cu31924052172271 



A CRITICAL EXPOSITION 



OF THE 



PHILOSOPHY OF LEIBNIZ. 



Hontion: C. J. CLAY and SONS, 
CAMBRIDGE UNIVERSITY PRESS WAREHOUSE, 

AVE MARIA LANE. 
BiBSBOin; 50, ■WELLINGTON STREET. 




ILeipjis: F. A. BBOOKHAUS. 

iSeto lotft: THE MAOMILLAN COMPANY. 

IBomfiB)): E. SEYMOUR HALE. 



3a itf^.^riApr 
A CRITICAL EXPOSITION 



OF THE 



PHILOSOPHY OF LEIBNIZ 



WITH AN 



APPENDIX OF LEADING PASSAGES _\ 



BY 

BERTRAND RUSSELL, M.A., 

FELLOW OE TKINITY OOLLEOE, OAMBEIEOE. 



' CAMBRIDGE: 
AT THE UNIVERSITY PRESS. 
2- 1900 3 



URIS LIBRARY 

AUG 1 ■? W89 



\A.ll Rights reserved.'} 




ffamititrge: 



PBINTED BY J. AND 0. F. OLAT, 
AT THE TJNIVEBSITT PRESS. 



PEEFACE. 



The history of philosophy is a study which proposes to 
itself two somewhat "different objects, of which the first is 
mainly historical, while the second is mainly philosophical. 
From this cause it is apt to result that, where we look for 
history of philosophy, we find rather history and philosophy. 
Questions concerning the influence of the times or of other 
philosophers, concerning the growth of a philosopher's 
system, and the causes which suggested his leading ideas — 
all these are truly historical : they require for their answer 
a considerable knowledge of the prevailing education, of the 
public to whom it was necessary to appeal, and of the scientific 
and political events of the period in question. But it may 
be doubted how far the topics dealt with in works where these 
elements predominate can be called properly philosophical. 
There is a tendency — which the so-called historical spirit has 
greatly increased — to pay so much attention to the relations 
of philosophies that the philosophies themselves are neglected. 
Successive philosophies may be compared, as we compare 
successive forms of a pattern or design, with little or. no 
regard to their meaning : an influence may be established by 
documentary evidence, or by identity of phrase, without any 
comprehension of the systems whose causal relations are under 
discussion. But there remains always a purely philosophical 
attitude towards previous philosophers — an attitude in which, 

62 



PREFACE. 



without regard to dates or influences, we seek simply to dis- 
cover what are the great types of possible philosophies, and 
guide ourselves in the search by investigating the systems 
advocated by the great philosophers of the past. There is 
still, in this inquiry — what is, after all, perhaps the most im- 
portant of the historical questions — the problem as to the 
actual views of the philosopher who is to be investigated. But 
these views are now examined in a different spirit. Where we 
are inquiring into the opinions of a truly eminent philosopher, 
it is probable that these opinions will form, in the main, a 
closely connected system, and that, by learning to understand 
them, we shall ourselves acquire knowledge of important philo- 
sophic truths. And since the philosophies of the past belong 
to one or other of a few great typ^s — types which in our own 
day are perpetually recurring — we may learn, from examining 
the greatest representative of any type, what are the grounds 
for such a philosophy. We may even learn, by observing the 
contradictions and inconsistencies from which no system hitherto 
propounded is free, what are the fundamental objections to 
the type in question, and how these objections are to be 
avoided. But in such inquiries the philosopher is no longer 
explained psychologically: he is examined as the advocate of 
what he holds to be a body of philosophic truth. By what 
process of development he came to this opinion, though in 
itself an important and interesting question, is logically irrele- 
vant to the inquiry how far the opinion itself is correct ; and 
among his opinions, when these have been ascertained, it 
becomes desirable to prune away such as seem inconsistent 
with his main doctrines, before those doctrines themselves are 
subjected to a critical scrutiny. Philosophic truth and false- 
hood, in short, rather than historical fact, are what primarily 
demand our attention in this inquiry. 

It is this latter task, and not the more strictly historical 
one, that I have endeavoured to perform towards Leibniz. The 



PREFACE. Vll 

historical task has been admirably performed by others, notably 
Professor Stein, in works to which I have nothing to add ; but 
the more philosophical task appears to be still unperformed. 
Erdmann's excellent account of Leibniz in his larger history 
(1842), from which I have learnt more than from any other 
commentary, was written in ignorance of the letters to Arnauld, 
and of much other important material which has been pub- 
lished since the date of Erdmann's edition of Leibniz (1840). 
And since his day, the traditional view of our philosopher's 
system appears to have been so deeply rooted in the minds of 
commentators that the importance of new manuscripts has 
not, I think, been duly recognized. Dillmann, it is true, has 
written a book whose object is similar to that of the present 
work, and has emphasized — rightly as it seems to me — the 
danger of obtaining our opinions of Leibniz from the Monad- 
ology. But it may be doubted whether Dillmann has suc- 
ceeded as well in understanding the meaning of Leibniz as in 
mastering the text of his writings. 

A few personal remarks may serve to explain why I believe 
a book on Leibniz to be not wholly uncalled for. In the Lent 
Term of 1899 I delivered a course of lectures on the Phi- 
losophy of Leibniz at Trinity College, Cambridge. In pre- 
paring these lectures, I found myself, after reading most of the 
standard commentators and most of Leibniz's connected trea- 
tises, still completely in the dark as to the grounds which 
had led him to many of his opinions. Why he thought that 
monads cannot interact; how he became persuaded of the 
Identity of Indiscemibles ; what he meant by the law of Suf- 
ficient Reason — these and many other questions seemed to 
demand an answer, but to find none. I felt — as many others 
have felt — that the Monadology was a kind of fantastic fairy 
tale, coherent perhaps, but wholly arbitrary. At this point 
I read the Biscours de Metaphysique and the letters to Arnauld. 
Suddenly a flood of light was thrown on all the inmost recesses 



viii PREFACE. 

of Leibaiz's philosophical edifice. I saw how its foundations 
were laid, and how its superstructure rose out of them. It 
appeared that this seemingly fantastic system could be de- 
duced from a few simple premisses, which, but for the con- 
clusions which Leibniz had drawn from them, many, if not 
most, philosophers would have been willing to admit. It seemed 
not unreasonable to hope that the passages which had seemed 
illuminating to me would seem so also to others. I have there- 
fore, in what follows, begun with the doctrines contained in 
these passages, and endeavoured as far as possible to exhibit 
the theory of monads as a rigid deduction from a small number 
of, premisses. The monad thus appears, not at the beginning 
of the exposition, but after a long preliminary chain of 
reasoning. And it must, I think, be allowed that, if this 
account be correct, Leibniz's value as a philosopher is very 
much greater than that which would result from the customary 
expositions. 

I have added an Appendix of classified extracts, in which 
it has been my object to include at least one definite pro- 
nouncement, wherever one could be found, on every point in 
Leibniz's philosophy. On moot points, or points on which he 
is inconsistent, I have in general given several quotations. 
I have given the date of a passage whenever it is not later 
than 1686, or seems important for some other reason. Passages 
referred to in the text are generally quoted in the corresponding 
paragraph of the Appendix, except when they have been already 
referred to and quoted in an earlier paragraph ; but passages 
quoted in the text are in general not repeated in the Appendix. 
For convenience of reference, I have made an index of the 
Appendix, so that any passage contained in it can be found 
at once by the reference. I have translated all passages quoted, 
and have nowhere assumed any knowledge of a foreign lan- 
guage. I have also endeavoured to assume no previous ac- 
quaintance with Leibniz beyond what can be pbtaiaed from 



PREFACE. IX 

Mr. Latta's excellent translations. In quoting passages trans- 
lated by him I have in general followed his translation; but 
the translations of Mr. Duncan and Mr. Langley I have usually 
found it necessary to correct. In quoting from the papers 
against Clarke, I have followed Clarke's translation wherever 
this is not seriously inaccurate. 

I have to thank Mr. G. E. Moore, of Trinity College, 
Cambridge, for reading the proofs and for many valuable 
suggestions, as also for the serious labour of revising all trans- 
lations from the Latin, both in the text and in the appendix. 
I have also to thank Professor James Ward for reading a 
portion of the work in manuscript and for several important 
criticisms. 



September, 1900. 



TABLE OF CONTENTS. 
CHAPTER I. 

LEIBNIZ'S PREMISSKS. 



1. Reasons why Leibniz never wrote a magnum 

2. Functions of the commentator on Leibniz 

3. Two types of inconsistency in his philosophy 

4. His premisses 

5. Course of the present work . . . . 

6. Influences which formed Leibniz's opinions . 



PAGE 

1 
2 
3 

4 
4 
5 



CHAPTER II. 

NECESSARY PROPOSITIONS AND THE LAW OF CONTRADICTION. 

7. Leibniz's philosophy begins with an analysis of propositions 8 

8. Outline of Leibniz's logical argument 9 

9. Questions raised by this argument 11 

10. Are all propositions reducible to the subject-predicate form? 12 

11. Analytic and synthetic propositions 16 

12. Necessity and contingency 23 



CHAPTER III. 

CONTINGENT PROPOSITIONS AND THE LAW OF SUFFICIENT 

REASON. 

13. The range of contingent judgments in Leibniz ... 25 

14. Meaning of the principle of sufficient reason ... 30 

15. Its relation to the law of contradiction 35 



XU CONTENTS. 



CHAPTER IV. 

THE CONCEPTION OF SUBSTANCE. 



16. Cartesian and Spinozistic views on substance 

17. The meaning of substance in Leibniz 

18. The meaning of activity 

19. Connection between activity and sufficient reason 

20. The states of one substance form one causal series 

21. How does a substance differ from the sum of its predicates? 48 

22. Relation of time to Leibniz's notion of substance . . 50 



PAGE 

40 
42 
44 
46 
47 



CHAPTER V. 

THE IDENTITY OF INDISCERNIBLES AND THE LAW OF 
CONTINUITY. POSSIBILITY AND COMPOSSIBILITY. 

"SSJ Meaning of the Identity of Indiscernibles .... 54 

24. The principle necessary, but not a premiss of Leibniz's 

philosophy .55 

25. Is Leibniz's proof of the principle valid? .... 58 
Every substance has an infinite number of predicates. Con- 
nection of this with contingency and with the identity of 
indiscernibles 60 

27. The Law of Continuity : three forms of continuity maintained 

by Leibniz 63 

28. Grounds of the Law of Continuity 65 

82) Possibihty and compossibility 66 

30. Common properties of all possible worlds .... 67 

31. The three kinds of necessity . 69 



CHAPTER VI. 

WHY DID LEIBNIZ BELIEVE IN AN EXTERNAL WORLD ? 

32. Leibniz accepted matter as a datum 70 

33. The existence of the external world has only "moral 

certainty" 72 



CONTENTS. 



XUl 



CHAPTER VII. 

THE PHILOSOPHY OF MATTER: (a) AS THE OUTCOME OF THE 
PRINCIPLES OF DYNAMICS. 



34. The general trustworthiness of perception is a premiss of 

Leibniz's philosophy 

35. Various meanings of matter and body 

36. Relation of Leibnizian and Cartesian Dynamics 

37. The essence of matter is not extension . 

38. Meaning of materia prima in Leibniz's Dynamics 

39. Materia secunda ...... 

40. The conception of force and the law of inertia 

41. Force and absolute motion .... 

42. Metaphysical grounds for assuming force 
4.3. Dynamical argument for plurality of causal series 

44. Three types of dynamical theory confused by Leibniz 

45. His grounds against extended atoms 

46. Against the vacuum 

47. And against action at a distance 

48. Force as conferring individuality 

49. Primitive and derivative force 

50. Antinomy of dynamical causation 



75 
75 
77 
77 
78 
80 
81 
84 
87 
89 
90 
92 
92 
93 
94 
95 
98 



CHAPTER VIII. 

THE PHILOSOPHY OF MATTER (CONTINUED), (b) AS EXPLAINING 
CONTINUITY AND EXTENSION. 



51. There must be simple substances, since there are compounds 100 

52. Extension, as distinguished from space, is Leibniz's starting- 

point 101 

53. Extension means repetition 102 

54. Hence the essence of a substance cannot be extension, since 

a substance must be a true unity 103 

55. The three kinds of point. Substances not material . . 104 

56. Motion is phenomenal, though force is real .... 106 



XIV CONTENTS. 

CHAPTER IX. 

THE LABYRINTH OF THE CONTINUUM. 

PAGE 

57. DifSculties about points 108 

58. Assertion of the actual infinite and denial of infinite number 109 

59. Continuity in one sense denied by Leibniz . . . . Ill 

60. In number, space, and time, the whole is prior to the part 112 

61. Space and time, for Leibniz, purely relational . . . 112 

62. Summary of the argument from the continuum to monads . 114 

63. Since aggregates are phenomenal, there is not really a 

number of monads 115 

64. DifiSculties of this view 116 

CHAPTER X. 

-- THE THEORY OF SPACE AND TIME AND ITS RELATION TO 

MONADISM. 

65. Reasons why a philosophy of substance must deny the 

reality of space 118 

66. Leibniz's arguments against the reality of space . . .119 

67. Leibniz's theory of position 120 

68. The relation of monads to space a fundamental difficulty of 

monadism 122 

69. Leibniz's early views on this subject 122 

70. His middle views 123 

71. His later views . 124 

72. Time and change 127 

73. Monadisms take an unsymmetrical view of the relations of 

space and of time to things 128 

74. Leibniz held confusedly to an objective counterpart of space 

and time 129 

CHAPTER XI. 

THE NATURE OF MONADS IN GENERAL. 

75. Perception i^-^ 

76. Appetition ]^33 

77. Perception not due to action of the perceived on the per* 

cipient I33 

78. Lotze's criticism of this view I35 

79. The pre-established harmony 13g 



CONTENTS. XV 

CHAPTER XII. 

SOUL AND BODY. 

FAan 

80. Relations of monads to be henceforth considered . . 139 

81. Cartesian and Spinozistic views of the relations of Soul and 

Body 139 

82. Outline of Leibniz's view 140 

83. The three classes of monads 141 

84. Activity and passivity 141 

85. Perfection and clearness of perception 142 

86. Materia prima as an element in each monad . . . 144 

87. Materia prima the source of finitude, plurality, and matter 145 

88. And of the interconnection of monads 146 

89. Two theories of soul and body in Leibniz .... 147 

90. First theory 147 

91. Second theory 149 

92. The vinculum substantiale 151 

93. The second theory to be rejected 152 

94. Preformation 154 



CHAPTER XIII. 

CONFUSED AND UNCONSCIOUS PERCEPTION. 

95. Two kinds of differences between monads .... 155 

96. Unconscious mental states ....... 156 

97. Confused and minute perceptions 157 



CHAPTER XIV. 
Leibniz's theory of knowledge. 



98. What theory of knowledge means .... 

99. Innate ideas and truths 

100. The New Essays inconsistent with Leibniz's metaphysics 

101. Difficulties as to innate ideas 

102. Distinction of sense and intellect 

103. The quality of ideas 

104. Definition . • . 

105. The Characteristica Universalis 



160 
161 
163 
165 
166 
167 
168 
169 



XVI CONTENTS. 



CHAPTER XV. 

PKOOFS OF THE EXISTENCE OF GOD. 

PAGE 

106. Four proofs allowed by Leibniz 172 

107. The ontological argument 172 

108. Proof that the idea of God is possible .... 174 

109. The cosmological argument 175 

110. Objections to this argument 176 

111. The argument from the eternal truths .... 177 

112. Its weakness 178 

113. Eelation of knowledge to truth 181 

114. Argument from the pre-established harmony . . .183 

115. Objections to this argument 185 

116. Inconsistencies resulting from Leibniz's belief in God . 186 

117. God's goodness . / 189 



CHAPTER XVI. 



LEIBNIZ S ETHICS. 



118. Freedom and determinism 

119. Psychology of volition and pleasure 

120. Sin 

121. Meaning of good and evil: three kinds of each . 

122. Metaphysical evil the source of the other two kinds 

123. Connection with the doctrine of analytic judgments 

124. The kingdoms of nature and of grace . 



191 
194 
196 
197 
198 
201 
201 



Appendix 205 



ABBREVIATIONS. 



G. Die philosophischen Schri/ten von G. W. Leibniz, heraus- 

gegeben von C. J. Gerhardt. Berlin, 1875 — 90. 

G. M. Leibnizens mathematische Schriften, herausgegeben von 
C. J. Gerhardt. Halle, 1850—63. 

F. de C. Bifutation inedite de Spinoza par Leibniz, prec6dee d'un 
memoire par A. Foucher de Careil. Paris, 1854. 

D. The PhUosophical Works of Leibnitz, with notes by 

George Martin Duncan. New Haven, 1890. 

L. Leibniz: The Monadology and other philosophical writings, 

translated, with introduction and notes, by Robert 
Latta. Oxford, 1898. 

N. E. New Essays concerning human understanding by Gott- 

fried Wilhelm Leibnitz, together with an Appendix 
consisting o/ some of his shorter pieces, translated by 
Alfred Gideon Langley. New York and London, 
1896. 



Ifo f. 



CHAPTER I. 



LEIBNIZ S PREMISSES. 



1. The philosophy of Leibniz, though never presented to 
the world as a systematic whole, was nevertheless, as a careful 
examination shows, an unusually complete and coherent system. 
As the method of studying his views must be largely dependent 
upon his method of presenting them, it seems essential to say 
something, however brief, as to his character and circumstances, 
and as to the ways of estimating how far any given work repre- 
sents his true opinions. 

The reasons why Leibniz did not embody his system in one 
great work are not to be found in the nature of that system. 
On the contrary, it would have lent itself far better than 
Spinoza's philosophy to geometrical deduction from definitions 
and axioms. It is in the character and circumstances of the 
man, not of his theories, that the explanation of his way of 
writing is to be found. For everything that he wrote he seems 
to have required some immediate stimulus, some near and 
pressing incentive. To please a prince, to refute a rival philo- 
sopher, or to escape the censures of a theologian, he would 
take any pains. It is to such motives that we owe the TModicde, 
the fmnciples of Nature and of Grace^, the Neiu Essays, and 
the Letters to Arnauld. But for the sole purposes of exposition 
he seems to have cared little. Few of his works are free from 
reference to some particular person, and almost all are more 
concerned to persuade readers than to provide the most valid 

1 Accepting Gerhardt's opinion that this work, and not the Monadology, 
was written for Prince Eugene (G. vi. 483). 

E. L. 1 



2 LEIBNIZ'S PREMISSES. 

arguments. This desire for persuasiveness must always be 
borne in mind in reading Leibniz's works, as it led him to give 
prominence to popular and pictorial arguments at the expense 
of the more solid reasons which he buried in obscurer writings. 
And for this reason we often find the best statement of his 
view on some point in short papers discovered among his 
manuscripts, and published for the first time by modern 
students, such as Erdmann or Gerhardt. In these papers we 
find, as a rule, far less rhetoric and far more logic than in his 
public manifestoes, which give a very inadequate conception 
of his philosophic depth and acumen. 

Another cause which contributed to the dissipation of his 
immense energies was the necessity for giving satisfaction to 
his princely employers. At an early age, he refused a profes- 
sorship at the University of Altdorf ', and deliberately preferred 
a courtly to an academic career. Although this choice, by 
leading to his travels in France and England, and making him 
acquainted with the great men and the great ideas of his age, 
had certainly a most useful result, it yet led, in the end, to an 
undue deference for princes and a lamentable waste of time in 
the endeavour to please them. He seems to have held himself 
amply compensated for laborious researches into the genealogy 
of the illustrious House of Hanover by the opportunities which 
such researches afforded for the society of the great. But the 
labours and the compensations alike absorbed time, and robbed 
him of the leisure which might have been devoted to the com- 
position of a magnum opus. Thus ambition, versatility, and 
the desire to influence particular men and women, all combined 
to prevent Leibniz from doing himself justice in a connected 
exposition of his system. 

2. By this neglect, the functions of the commentator are 
rendered at once more arduous and more important than in 
the case of most philosophers. What is first of all required in 
a commentator is to attempt a reconstruction of the system 
which Leibniz should have written — to discover what is the 
beginning, and what the end, of his chains of reasoning, to 
exhibit the interconnections of his various opinions, and to fill 
in from his other writings the bare outlines of such works as 
' Guhrauer, Leibnitz: Eine Biographie, Vol. i. p. 44. 



LEIBNIZ S, PREMISSES. 3 

the Monadology or the Discours de Metaphysique. This un- 
avoidable but somewhat ambitious attempt forms one part — 
perhaps the chief part — of my purpose in the present work. 
To fulfil it satisfactorily would be scarcely possible, and its 
necessity is my only excuse' for the attempt. As I wish to 
exhibit a coherent whole, I have confinjd myself, as far as 
possible, to Leibniz's mature views — to the views, that is, 
which he held, with but slight modifications, from January 
1686 till his death in 1716. His earlier views, and the 
influence of other philosophers, have been considered only in 
so far as they seemed essential to the comprehension of his 
final system. 

But, in addition to the purely historical purpose, the present 
work is designed also, if possible, to throw light on the truth or 
falsity of Leibniz's opinions. Having set forth the opinions 
which were actually held, we can hardly avoid considering how 
far they are mutually consistent, and hence — since philosophic 
error chiefly appears in the shape of inconsistency — how far the 
views held were true. Indeed, where there is inconsistency, a 
mere exposition must point it out, since, in general, passages 
may be found in the author supporting each of two opposing 
views. Thus unless the inconsistency is pointed out, any view 
of the philosopher's meaning may be refuted out of his own 
mouth. Exposition and criticism, therefore, are almost insepa- 
rable, and each, I believe, suffers greatly from the attempt at 
separation. 

3. The philosophy of Leibniz, I shall contend, contains 
inconsistencies of two kinds. One of these kinds is easily 
removed, while the other is essential to any philosophy re- 
sembling that of the Monadology. The first kind arises solely 
through the fear of admitting consequences shocking to the 
prevailing opinions of Leibniz's time — such are the main- 
tenance of sin and of the ontological argument for God's 
existence. Where such inconsistencies are found, we, who do 
not depend upon the smiles of princes, may simply draw the 
consequences which Leibniz shunned. And when we have 
done this, we shall find that Leibniz's philosophy follows 
almost entirely from a small number of premisses.^ The 
proof that his system does follow, correctly and necessarily, 

1—2 



4 LEIBNIZ S PEEMISSES. 

from these premisses, is the evidence of Leibniz's philosophical 
excellence, and the permanent contribution which he made 
to philosophy. But it is in the course of this deduction that 
we become aware of the second and greater class of inconsist- 
encies. The premisses themselves, though at first sight com- 
patible, will be found, in the course of argument, to lead to 
contradictory results. We are therefore forced to hold that 
one or more of the premisses are false. I shall attempt to 
prove this from Leibniz's own words, and to give grounds for 
deciding, in part at least, which of his premisses are erroneous. 
In this way we may hope, by examining a system so careful 
and so thorough as his, to establish independent philosophical 
conclusions which, but for his skill in drawing deductions, 
might have been very difficult to discover. 

4. The principal premisses of Leibniz's philosophy appear 
to me to be five. Of these some were by him definitely laid 
down, while others were so fundamental that he was scarcely 
conscious of them. I shall now enumerate these premisses, 
and shall endeavour to show, in subsequent chapters, how the 
rest of Leibniz follows from them. The premisses in question 
are as follows : 

I. Every proposition has a subject and a predicate. 

II. A subject may have predicates which are qualities 

existing at various times. (Such a subject is called 
a substance.) 

III. True propositions not asserting existence at particular 

times are necessary and analytic, but such as assert 
existence at particular times are contingent and 
synthetic. The latter depend upon final causes. 

IV. The Ego is a substance. 

V. Perception yields knowledge of an external world, ie. 

of existents other than myself and my states. 
The fundamental objection to Leibniz's philosophy will be 
found to be the inconsistency of the first premiss with the 
fourth and fifth ; and in this inconsistency we shall find a 
general objection to Monadism. 

5. The course of the present work will be as follows : 
Chapters II. — V. will discuss the consequences of the first four 
of the above premisses, and will show that they lead to the 



LEIBNIZ S PREMISSES. 5 

whole, or nearly the whole, of the necessary propositions of the 
system. Chapters VI. — XL will be concerned with the proof 
and description of Leibniz's Monadism, in so far as it is inde- 
pendent of final causes and the idea of the good. The remain- 
ing chapters will take account of these, and will discuss Soul 
and Body, the doctrine of God, and Ethics. In these last 
chapters we shall find that Leibniz no longer shows great 
originality, but tends, with slight alterations of phraseology, to 
adopt (without acknowledgment) the views of the decried 
Spinoza. We shall find also many more minor inconsistencies 
than in the earlier part of the system, these being due chiefly 
to the desire to avoid the impieties of the Jewish Atheist, and 
the still greater impieties to which Leibniz's own logic should 
have led him. Hence, although the subjects dealt with in the 
last five chapters occupy a large part of Leibniz's writings, they 
are less interesting, and will be treated more briefly, than the 
earlier and more original portions of his reasoning. For this 
there is the additional reason that the subjects are less funda- 
mental and less difiicult than the subjects of the earlier 
chapters. 

6. The influences which helped to form Leibniz's philo- 
sophy are not directly relevant to the purpose of the present 
work, and have, besides, been far better treated by commen- 
tators^ than the actual exposition of his final system. Never- 
theless, a few words on this subject may not be amiss. Four 
successive schools of philosophy seem to have contributed to 
his education ; in all he found something good, and from each, 
without being at any time a mere disciple, he derived a part of 
his views. To this extent, he was an eclectic ; but he differed 
from the usual type of eclectic by his power of transmuting 
what he borrowed, and of forming, in the end, a singularly 
harmonious whole. The four successive influences were : Scho- 
lasticism, Materialism, Cartesianism, and Spinozism. To these 
we ought to add a careful study, at a critical period, of some of 
Plato's Dialogues. 

' See especially Gnhrauer, Leibnitz : Sine Biographie, Breslau, 1846 ; Stein, 
Leibniz und Spinoza, BerUn, 1890; Selver, Entwicklungsgang der Leibnizschen 
Monadenlehre, Leipzig, 1885 ; Tonnies, Leibniz und Hobbes, Phil. Monatshefte, 
Vol. XXIII. ; Trendelenburg, Historische Beitrage, Vol. ii., Berlin, 1855. 



LEIBNIZ*S PREMISSES. 

Leibniz was educated in the scholastic tradition, then still 
unbroken at most of the German universities. He obtained a 
competent knowledge of the schoolmen, and of the scholastic 
Aristotle', while still a boy; and in his graduation thesis, De 
Principio Individui, written in 1663, he still employs the 
diction and methods of scholasticism. But he had already, two 
years before this time (if his later reminiscences are to be 
trusted), emancipated himself from what he calls the " trivial 
schools^," and thi'own himself into the mathematical material- 
ism of the day. Gassendi and Hobbes began to attract him, 
and continued (it would seem) greatly to influence his specula- 
tions until his all-important journey to Paris. In Paris (with 
two brief visits to England) he lived from 1672 to 1676, and 
here he became acquainted, more intimately than he could in 
Germany, with Cartesianism both in mathematics and philo- 
sophy — with Malebranche, with Arnauld the Jansenist theolo- 
gian, with Huygens, with Robert Boyle, and with Oldenburg, 
the Secretary of the Royal Society. With these men he carried 
on correspondence, and through Oldenburg some letters (the 
source of 150 years of controversy') passed between him and 
Newton. It was during his stay in Paris that he invented 
the Infinitesimal Calculus, and acquired that breadth of learn- 
ing, and that acquaintance with the whole republic of letters, 
which afterwards characterized him. But it was only on his 
way back from Paris that he learnt to know the greatest man- 
of the older generation. He spent about a month of the year 
1676 at the Hague, apparently in constant intercourse with 
Spinoza; he discussed with him the laws of motion and the 
proof of the existence of God, and he obtained a sight of part 
(at any rate) of the Ethics in manuscripts When the Ethics 
soon afterwards was posthumously published, Leibniz made 
notes of it, and undoubtedly bestowed very careful thought 

1 Leibniz appears, in spite of the great influence which Aristotle exerted 
upon him, to have never studied him carefully in the original. See Stein op. 
cit. p. 163 ff. 

" Guhrauer, Leibnitz, Vol. i. pp. 25, 26; G, in. 606. 

8 These letters were said, by Newton's friends, to have given Leibniz the 
opportunity for plagiarizing the Calculus — a charge now known to be abso- 
lutely groundless, 

* See Stein, Leibniz nnd Spinoza, Chapter iv. 



LEIBNIZ S PREMISSES. 7 

upon its demonstrations. Of his thoughts during the years 
which followed, down to 1684 or even 1686 (since the Thoughts 
on Knowledge, Truth and Ideas deal only with one special 
subject), only slight traces remain, and it seems probable that, 
like Kant in the years from 1770 to 1781, he was in too much 
doubt to be able to write much. He certainly read Plato', and 
he certainly desired to refute Spinoza. At any rate, by the 
beginning of 1686 he had framed his notion of an fndividual 
substance, and had sufficiently perfected his philosophy to send 
Arnauld what is perhaps the best account he ever wrote of 
it;r-I mean the Biscours de Mdtaphysique (G. iv. 427 — 463). 
With this and the letters to Arnauld his mature philosophy 
begins; and not only the temporal, but the logical beginning 
also is, in my opinion, to be sought here. The argument 
which forms the logical beginning, and gives the definition of 
substance, will be found in the four following chapters. 

1 Cf. Stein, op. cit. p. 119. 



CHAPTEE II. 



NECESSARY PEOPOSITIONS AND THE LAW OF CONTRADICTION. 

7. That all sound philosophy should begin with an analysis 
of propositions, is a truth too evident, perhaps, to demand a 
proof. That Leibniz's philosophy began with such an analysis, 
is less evident, but seems to be no less true. The system, 
which he afterwards uniformly maintained, was completed, in 
all essentials, by the beginning of the year 1686. In his 
writings during this year, when the grounds of his new opinions 
were still freshly present to his mind, there occurs an argument 
of great importance, derived, as he himself says (G. ii. 73), from 
the general nature of propositions, and capable, in his opinion, 
if the plurality of substances be admitted, of alone establishing 
the remainder of his system. This argument is to be found in 
the letters to Arnauld, in the Discours de Mitaphysique, written 
for Arnauld in January, 1686 (G. iv. 427 — 463)', and in a 
short undated paper, entitled Specimen Inventorum de Admi- 
randis naturae generalis arcanis (G. vii. 309 — 318). Although 
the same reasoning does not, so far as I am aware, occur 
explicitly in any other passages, it is often suggested^, and is 
alone capable of explaining why Leibniz held that substances 
do not interact. That Xieibniz did not repeat, in his published 
works, this purely logical argument, is explained, in view of his 
invariable habit of choosing the reasons most likely to convince 
his readers, bj' a passage in one of his letters to Arnauld (G. ii. 
73, 74). " I expected," he writes, " that the argument drawn 

1 See G. II. 11 it; also iv. 409, 410. 

2 e.g. L. 326 ; G. iv. 496. 



THE LAW OF CONTRADICTION. 9 

from the general nature of propositions would make some 
impression on your mind ; but I confess also that few people 
are capable of appreciating such abstract truths, and that 
perhaps no one but you would have so easily perceived its 
force." We know, however, that Leibniz often expressed an 
intention of publishing his correspondence with Arnauld (G. ii. 
10), and must, consequently, have regarded this correspondence 
as adequately expressing his philosophical opinions. There is 
thus no reason to suppose that, after the date of these letters, 
his views on fundamental points underwent any serious 
alteration. 

The argument in question, whose examination will occupy 
the present and the three following chapters, yields the whole, 
or nearly the whole, of the necessary part of Leibniz's philo- 
sophy — of the propositions, that is to say, which are true of ajl 
possible worlds. In order to obtain further the propositions 
describing the actual world, we need the premiss that per- 
ception gives knowledge of an external world, whence follow 
space and matter and the plurality of substances. iThis 
premiss is derived, apparently, from no better basis than 
common sense, and with its introduction, in Chapter VI., we 
shall pass to a new division of Leibniz's philosophy. But 
since the meaning of substance is logically prior to the dis- 
cussion of the plurality or the perceptions of substances, it is 
plain that the present argument, from which the meaning of 
substance is derived, must first be expounded and examined. 
I shall first state the argument quite briefly, and then proceed 
to set forth its various parts in detail. 

8. Every proposition is ultimately reducible to one which 
attributes a predicate to a subject. In any such proposition, 
unless existence be the predicate in question, the predicate is 
somehow contained in the subject. The subject is defined by 
its predicates, and would be a different subject if these were 
different. Thus every true judgment of subject and predicate 
is analytic — i.e. the predicate forms part of the notion of the 
subject — unless actual existence is asserted. Existence, alone 
among predicates, is not contained in the notions of subjects 
which exist. Thus existential propositions, except in the case 
of God's existence, are synthetic, i.e. there would be no contra- 



10 THE LAW OF CONTRADICTION. 

diction if the subjects which actually do exist did not exist. 
Necessary propositions are such as are analytic, and synthetic 
propositions are always contingent. 

When many predicates can be attributed to one and the 
same subject, while this subject cannot be made the predicate 
of any other subject, then the subject in question is called an 
individual substance. Such subjects involve, sub ratione possi- 
bilitatis, a reference to existence and time; they are possible 
existents, and they have predicates expressing their states at 
different times. Such predicates are called contingent or 
concrete predicates, and they have the peculiarity that no one 
of them follows analytically from any others, as rational follows 
from human. Thus when a subject is defined by means of a 
certain number of such predicates, there is no contradiction in 
supposing it to be without the remainder. Nevertheless, in 
the subject which has these predicates, they are all contained, 
so that a perfect knowledge of the subject would enable us to 
deduce all its predicates. Moreover there is a connection, 
though not a necessary one, between the various concrete 
predicates; sequences have reasons, though these incline 
without necessitating. The need of such reasons is the prin- 
ciple of sufficient reason. Subjects whose notion involves a 
reference to time are required by the idea of persistence. 
Thus in order to say that I am the same person as I was, we 
require, not merely internal experience, but some ct, priori 
reason. This reason can only be that I am the same subject, 
that my present and past attributes all belong to one and the 
same substance. Hence attributes which exist in different 
parts of time must be conceived, in such a case, as attributes of 
the same subject, and must therefore be contained, somehow, 
in the notion of the subject. Hence the notion of me, which 
is timeless, involves eternally all my states and their connec- 
tions. Thus to say, all my states are involved in the notion of 
me, is merely to say, the predicate is in the subject. Every 
predicate, necessary or contingent, past, present or future, is 
comprised in the notion of the subject. From this proposition 
it follows, says Leibniz, that every soul is a world apart; for 
every soul, as a subject, has eternally, as predicates, all the 
states which time will bring it ; and thus these states follow 



THE LAW OF CONTRADICTION. 11 

from its notion alone, without any need of action from without. 
The principle, according to which the states of a substance 
change, is called its activity ; and since a substance is essentially 
the subject of predicates which have a reference to time, 
activity is essential to every substance. The notion of an 
individual substance differs from a mere collection of general 
notions by being complete, as Leibniz puts it, i.e. by being 
capable of wholly distinguishing its subject, and involving 
circumstances of time and place. The nature of an individual 
substance, he says, is to have so complete a notion as to suffice 
for comprehending and deducing all its predicates. Hence he 
concludes that no two substances can be perfectly alike. { From 
this stage, by the help of the empirical premiss mentioned 
above, the doctrine of monads follows easily. 

9. Such is, in outline, the logical argument by which 
Leibniz obtains his definition of an individual substance. In 
the above brief account, I have made no endeavour to conceal 
the gaps and assumptions involved. We must now enquire 
whether the gaps can be filled and the assumptions justified. 
For this purpose the following seem to be the most important 
questions. 

(1) Are all propositions reducible to the subject-predicate 

form ? 

(2) Are there any analytic propositions, and if so, are these 

fundamental and alone necessary ? 

(3) What is the true principle of Leibniz's distinction 

between necessary and contingent propositions ? 

(4) What is the meaning of the principle of sufficient 

reason, and in what sense do contingent propositions 
depend upon it ? 

(5) What is the relation of this principle to the Law of 

Contradiction ? 

(6) Does the activity of substance unduly presuppose 

time? 

(7) Is there any validity in Leibniz's deduction of the 

Identity of Indiscernibles ? 
It is only by a critical discussion of these points that 
Leibniz's meaning can be grasped; for unless we have clear 
ideas ahont philosophy, we cannot hope to have clear ideas 



12 THE LAW OF CONTRADICTION. 

about Leibniz's philosophy. When all these questions have 
been discussed, we may proceed to enquire why Leibniz be- 
lieved in a plurality of substances, and why he held that each 
mirrored the universe. But until we are clear as to his logic, 
we cannot hope to understand its applications. 

10. The question whether all propositions are reducible to 
the subject-predicate form is one of fundamental importance to 
all philosophy, and especially to a philosophy which uses the 
notion of substance. For this notion, as we shall see, is 
derivative from the logical notion of subject and predicate. 
The view that a subject and a predicate are to be found in 
every proposition is a very ancient and respectable doctrine ; it 
has, moreover, by no means lost its hold on philosophy, since 
Mr Bradley's logic consists almost wholly of the contention 
that every proposition ascribes a predicate to Reality, as the 
only ultimate subject'. The question, therefore, whether this 
form is universal, demands close attention, not only in con- 
nection with Leibniz, but also in connection with the most 
modern philosophy. I cannot here, however, do more than 
indicate the grounds for rejecting the traditional view. 

The plainest instances of propositions not so reducible are 
the propositions which employ mathematical ideas. All asser- 
tions of numbers, as e.g. " There are three men," essentially 
assert plurality of subjects, though they may also give a 
predicate to each of the subjects. Such propositions cannot be 
regarded as a mere sum of subject-predicate propositions, since 
the number only results from the singleness of the proposition, 
and would be absent if three propositions, asserting each the 
presence of one man, were juxtaposed. Again, we must admit, 
in some cases, relations between subjects — e.g. relations of 
position, of greater and less, of whole and part. To prove that 
these are irreducible would require a long argument, but may 
be illustrated by the following passage from Leibniz himself 
(D. pp. 266—7; G. vii. 401): 

" The ratio or proportion between two lines L and M may 

be conceived three several ways ; as a ratio of the greater L to 

the lesser M ; as a ratio of the lesser M to the greater L ; and 

lastly, as something abstracted from both, that is, as the ratio 

' Of. Logic, Book I. Chap, n., especially pp. 49, 50, 66. 



THE LAW OF CONTRADICTION. 13 

between L and M, without considering which is the ante- 
cedent, or which the consequent ; which the subject, and which 
the object.... In the first way of considering them, L the 
greater is the subject, in the second M the lesser is the subject 
of that accident which philosophers call relation or ratio. But 
which of them will be the subject, in the third way of consider- 
ing them? It cannot be said that both of them, L and M 
together, are the subject of such an accident; for if so, we 
should have an accident in two subjects, with one leg in one, 
and the other in the other ; which is contrary to the notion of 
accidents. Therefore we must say that this relation, in this 
third way of considering it, is indeed out of the subjects ; but 
being neither a substance, nor an accident, it must be a mere 
ideal thing, the consideration of which is nevertheless useful." 

This passage is of capital importance for a comprehension 
of Leibniz's philosophy. After he has seemed, for a moment, to 
realize that relation is something distinct from and independent 
of subject and accident, he thrusts aside the awkward discovery, 
by condemning the third of the above meanings as " a mere 
ideal thing." If he were pushed as to this " ideal thing," I am 
afraid he would declare it to be an accident of the mind which 
contemplates the ratio. It appears plainly from his discussion 
that he is unable to admit, as ultimately valid, any form of' 
judgment other than the subject-predicate form, although, in 
the case he is discussing, the necessity of relational judgments 
is peculiarly evident. 

It must not be supposed that Leibniz neglected relational 
propositions. On the contrary, he dealt with all the main 
types of such propositions, and endeavoured to reduce them to 
the subject-predicate forn>. This endeavour, as we shall see, 
was one of the main sources of most of his doctrines. Mathe- ^ 
matician as he was, he could hardly neglect space, time and 
numUer. As regards propositions asserting numbers, he held 
aggregates to be mere phenomena: they are what he calls 
" semi-mental entities." Their unity, which is essential to the 
assertion of any number, is, he says, added by perception alone, 
by the very fact of their being perceived at one time (G. ii. 
.517). All that is true, then, in such judgments, is the indi- 
vidual assertions of subject and predicate, and the psychological 



14 THE LAW OF CONTRADICTION. 

assertion of simultaneous perception as a predicate of the 
percipient. Again, we are told that numbers have the nature 
of relations, and hence are in some manner beings (G. ii. 304). 
But relations, though founded in things, derive their reality 
from the supreme reason (N. E. p. 235 ; G. v. 210) ; God sees 
not only individual monads and their various states, but their 
relations also, and in this consists the reality of relations (G. II. 
438). And as regards space and time, Leibniz always en- 
deavoured to reduce them to attributes of the substances in 
them. Position, he says, like priority or posteriority, is nothing 
but a mode of a thing (G. ii. 347). The whole doctrine is 
collected in the Ne^u Essays (N. E. p. 148 ; G. v. 132). " Units 
are separate, and the understanding gathers them together, 
however dispersed they may be. Yet, although relations are 
from the understanding, they are not groundless or unreal. 
For the primitive understanding is the origin of things; and 
indeed the reality of all things, simple substances excepted, 
consists only in the foundation of the perceptions of phenomena 
in simple substances." Thus relations and aggregates have 
only a mental truth ; the true proposition is one ascribing 
a predicate to God and to all others who perceive the re- 
lation'. 

Thus Leibniz is forced, in order to maintain the subject- 
predicate doctrine, to the Kantian theory that relations, though 
veritable, are the work of the mind. As applied to various 
special relations — as e.g. those of space, time, and number — I 
shall criticize special forms of this doctrine in their proper 
places. The view, implied in this theory, and constituting a 
large part of Kant's Copernican revolution, that propositions 
may acquire truth by being believed^, will be criticized in 
connection with the deduction of God's existence from the 
eternal truths. But as applied to relations, the view has, in 
Leibniz's case, a special absurdity, namely, that the relational 
propositions, which God is supposed to know, must be strictly 
meaningless. The only ground for denying the independent 

' Cf. Lotze, Metaphysic, beginning of § 109. 

^ I am aware that this is not an orthodox statement of the Kantian theory. 
The kind of grounds which lead me to think it correct, will be found indicated 
in Chaps. XIV. and XV., especially § 113. 



THE LAW OF CONTRADICTION. 15 

reality of relations is, that propositions must have a subject and ' 
a predicate. If this be so, a proposition without a subject and 
a predicate must be no proposition, and must be destitute of 
meaning. But it is just such a proposition which, in the case 
of numbers, or of relations between monads, God is supposed 
to see and believe. God, therefore, believes in the truth of 
what is meaningless. If the proposition which he believes, on 
the other hand, be truly a proposition, then there are proposi- 
tions which do not have a subject and a predicate. Thus the 
attempt to reduce relations to predicates of the percipient 
sufifers from one or other of two defects. Either the percipient 
is deceived into seeing truth in a meaningless form of words, or 
there is no reason to suppose the truth dependent upon his 
perception of it. 

A thorough discussion of the present question would, at ■ 
this point, proceed to show that judgments of subject and 
predicate are themselves relational, and include, moreover, as 
usually understood, two fundamentally different types of rela- 
tion. These two types are illustrated by the two propositions : 
"This is red," and "red is a colour." In showing that these 
two propositions express relations, it would be shown that 
relation is more fundamental than the two special types of 
relation involved. But such a discussion is beset with diffi- 
culties, and would lead us too far from the philosophy of 
Leibniz. 

In the belief that propositions must, in the last analysis, 
have a subject and a predicate, Leibniz does not differ either 
from his predecessors or from his successors. Any philosophy 
which uses either substance or the Absolute will be found, on 
inspection, to depend upon this belief Kant's belief in an 
unknowable thing-in-itself was largely due to the same theory. 
It cannot be denied, therefore, that the doctrine is important. 
Philosophers have differed, not so much in respect of belief in 
its truth, as in respect of their consistency in carrying it out. 
In this latter respect, Leibniz deserves credit. But. his assump- 
tion of a plurality of substances made the denial of relations 
peculiarly difficult, and involved him in all the paradoxes of the 
pre-established harmony'. 

' Cf. Bradley, Appearance and Reality, Ist ed. pp. 29 — 30. 



16 THE LAW OF CONTBADICTION. 

11. I pass now to a question which is no less fundamental, 
and more difficult, than that which we have just discussed. 
This is the question — as it has been called since Kant — of 
analytic and synthetic judgments and their relation to ne- 
cessity. Leibniz's position on this question determined, not 
only his departure from his predecessors, but also, by its 
obvious untenability, Kant's great departure from, him.; On 
this point it will be necessary to begin with an account of 
Leibniz's views. 

Two questions must be earefuHy distinguished in this 
connection. The first concerns the meaning and range of 
analytic judgments, the second concerns their claim to exclusive 
necessity. On the second question, Leibniz agreed wholly with 
his predecessors ; on the first, by the discovery that all causal 
laws are syuthetic, he made an important change, which pre- 
pared the way for Kant's discovery that all the propositions of 
Mathematics are synthetic. 

In discussing the first of these questions, I shall use the 
terms analytic and synthetic, though they are not used by 
Leibniz in this sense. ; He uses the terms necessary and con- 
tingent ; but this use prejudges, in his own favour, the second 
question, which forms one of the principal issues between him 
and Kant. It is therefore unavoidable to depart from Leibniz's 
usage, since we need two pairs of terms, where he required only 
one pair. 

As regards the range of analytic judgments, Leibniz held 
that all the propositions of Logic, Arithmetic and Geometry 
are of this nature, wh^le all existential propositions, except 
the existence of God, are synthetic. The discovery which 
determined his views on this point was, that the laws of 
motion, and indeed all causal laws (though not, as I shall 
show in the next chapter, the law of Causality itself), are 
synthetic, and therefore, in his system, also contingent (c£ 
G. III. 645). 

As regards the meaning of analytic judgments, it will assist 
us to have in our minds some of the instances which Leibniz 
suggests. We shall find that these instances suffer from one 
or other of two defects. Either the instances can be easily 
seen to be not truly analytic — this is the case, for example, in 



THE LAW OF CONTRADICTION. 17 

Arithmetic and Geometry — or they are tautologous, and so not 
properly propositions at all. Thus Leibniz says, on one occa- 
sion (N. E. p. 404 ; G. v. 343), that primitive truths of reason 
are identical, because they appear only to repeat the same 
thing, without giving any information. One wonders, in this 
case, of what use they can be, and the wonder is only increased 
by the instances which he proceeds to give. Among these are 
"A is A," "I shall be what I shall be," "The equilateral 
rectangle is a rectangle," or, negatively, " A B cannot be non-A." 
Most of these instances assert nothing; the remainder can 
hardly be considered the foundations of any important truth. 
Moreover those which are true presuppose, as I shall now show, 
more fundamental propositions which are synthetic. To prove 
this, we must examine the meaning of analytic judgments, and 
of the definitions which they presuppose. 

The notion that all d priori truths are analytic is essentially 
connected with the doctrine of subject and predicate. An 
analytic judgment is one in which the predicate is contained in 
the subject. The subject is supposed defined by a number of 
predicates, one or more of which are singled out for predication 
in an analytic judgment. Thus Leibniz, as we have just seen, 
gives as an instance the proposition: "The equilateral rectangle 
is a rectangle " (N. E. p. 405 ; G. v. 343). In the extreme 
case, the subject is merely reasserted of itself, as in the propo- 
sitions: "A is A," "I shall be what I shall be" (ib.). Now two 
points seem important in this doctrine. In the first place, the 
proposition must be of what I distinguished above as the 
second type of subject-predicate proposition, i.e. of the type 
" red is a colour," " man is rational," not of the type " this is 
red," or " Socrates is human." That is to say, the proposition 
is concerned with the relation of genus and species, not of 
species and individual. This is the reason why every proposi- 
tion about actual individuals is, in Leibniz's opinion, contingent. 
I do not wish at present to discuss whether the distinction of 
these two types is ultimately tenable — this question will be 
better discussed when we come to the Identity of Indiscernibles. 
For the present, I only wish to point out, what Leibniz 
frequently asserts, that analytic propositions are necessarily 
concerned with essences and species, not with assertions as to 
R r,. , 2 



18 THE LAW OP CONTRADICTION. 

individuals 1. The second point concerning analytic propo- 
sitions is, that the subject, except in such pure tautologies as 
" A is A," must always be complex. The subject is a collec- 
tion of attributes, and the predicate is a part of this collection. 
If, however, the reference to individuals be deemed essential to 
the distinction of subject from predicate, we shall have to say 
that the subject is any individual having a certain collection of 
predicates. In this way, we might attempt to reduce the 
second type to the first. But now the proposition becomes 
hypothetical : " If a thing is red, it is coloured." This Leibniz 
admits. The eternal truths, he says, are all hypothetical, 
and do not assert the existence of their subjects (N. E. 
p. 515; G. V. 428). But this makes it evident that our reduc- 
tion to the first type has failed. The above hypothetical 
proposition evidently presupposes the proposition "red is a 
colour"; and thus Leibniz goes on to say that the truth of 
hypothetical propositions lies in the connection of ideas (N. E. 
p. 516 ; G. V. 429). Thus in analytic judgments, when they 
are not expressed in the derivative hypothetical form, the 
subject is a complex idea, i.e. a collection of attributes, while 
the predicate is some part of this collection. 

The collection, however, — and this is the weak point of the 
doctrine of analytic judgments — must not be any haphazard 
collection, but a collection of compatible or jointly predicable 
predicates (predicability being here of the first type). Now 
this compatibility, since it is presupposed by the analytic 
judgment, cannot itself be analytic. This brings us to the 
doctrine of definition, in which we shall find that Leibniz, like 
, all who have held analytic propositions to be fundamental, was 
guilty of much confusion. 

Definition, as is evident, is only possible in respect of 
complex ideas. It consists, broadly speaking, in the analysis 
of complex ideas into their simple constituents. Since one idea 
can only be defined by another, we should incur a vicious circle 
if we did not admit some indefinable ideas. This obvious truth 

1 Foueher de Careil, Refutation in^dite de Spinoza par Leibniz, Paris, 1854 
p. 24 (D. 175) ; G. V. 268 (N. B. 309) ; G. n. 49. In this latter passage, it is 
specially instructive to observe Leibniz's oorreetions, as indicated in Gerhardt's 
notes. 



THE LAW OF CONTRADICTION. 19 

is fully recognized by Leibniz, and the search for the simple 
ideas, which form the presuppositions of all definition, consti- 
tutes the chief part of his studies for the Universal Charac- 
teristic. Thus Leibniz says {Monadology, §§ 33, 35) : " When a ~ 
truth is necessary, its reason can be found by analysis, resolving 
it into more simple ideas and truths, until we come to those 
which are primary.... In short, there are simple ideas, of 
which no definition can be given; there are also axioms and 
postulates, in a word, primary principles, which cannot be 
proved, and indeed have no need of proof; and these are 
identical propositions, whose opposite involves an express 
contradiction" (L. 236—7; D. 223; G. vi. 612). The same 
view is expressed whenever Leibniz treats of this question. 
What I wish to show is, that Leibniz's theory of definition, as ^^ 
consisting of analysis into indefinable simple ideas, is inconsis- 
tent with the doctrine that the " primary principles " are 
identical or analytic ; and that the former is correct, while the 
latter is erroneous. 

Leibniz often urges that the objects of definitions must be 
shown to be possible. It is thus that he distinguishes what he 
calls real definitions from such as are only nominal {e.g. D. 
p. 30; G. IV. 424). And thus he says that Arithmetic is 
analytic, because the number 3, for example, is defined as 2 -t- 1, 
but he confesses that 3, so defined, must be seen to be possible 
(N. E. p. 410 ; G. v. 347). In one passage (G. i. p. 385), he even 
confesses that ideas in general involve a judgment, namely the 
judgment that they are possible. This confession, one might 
suppose, would be inconsistent with the doctrine of analytic 
judgments; it is rendered consistent, however, by Leibniz's 
definition of possibility. A possible idea, for him, is one which 
is not self-contradictory. But if this were all that is meant, 
any collection of simple ideas would be compatible, and there- 
fore every complex idea would be possible. In an early proof 
of the existence of God (G. vii. 261) submitted by Leibniz to 
Spinoza at the Hague, this argument is actually used to show 
that God is possible^ He here defines God as the subject 

1 We shall find, when we come to deal with the proofs of God's existence, 
that this paper, in spite of its early date (1676), contains no views which 
Leibniz did not hold in his maturity. 

2—2 



20 THE LAW OF CONTRADICTION. 

which has all positive predicates. He takes two simple predi- 
cates, A and B, and shows, what is sufficiently evident, that 
they cannot be mutually contradictory. Hence he concludes 
that God, so defined, is possible. But since all ideas, when 
correctly analyzed, must, for Leibniz, be ultimately predicates, 
or collections of predicates, it follows that all ideas will be 
possible. And indeed, as Leibniz himself urges in this proof, 
any relation between simple ideas is necessarily synthetic. 
For the analytic relation, as we saw, can only hold between 
' ideas of which one at least is complex. Hence if there were no 
synthetic relations of compatibility and incompatibility, all 
complex ideas would be equally possible. Thus there is always 
involved, in definition, the synthetic proposition that the simple 
constituents are compatible. If this be not the case, the 
constituents are incompatible — e.g. good and bad, or two 
different magnitudes of the same kind — and this is also a 
synthetic relation, and the source of negative propositions'. 

This conclusion may be enforced by examining some idea 
which is self-contradictory, such as a round square. In order 
that an idea may be self-contradictory, it is evidently necessary 
that it should involve two judgments which are mutually 
contradictory, i.e. the truth and falsehood of some judgment. 
For the Law of Contradiction applies, not to ideas, but to 
judgments: it asserts that every proposition is true or false 
(N. E. p. 405 ; G. v. 343). Hence a mere idea, as such, cannot 
be self-contradictory. Only a complex idea which involves 
at least two propositions can be self-contradictory. Thus the 
idea "round square" involves the proposition "round and 
square are compatible," and this involves the compatibility of 
having no angles, and of having four angles. But the contra- 
diction is only possible because round and square are both 
complex, and round and square involve synthetic propositions 
asserting the compatibility of their constituents, while round 

1 Leibniz seems to have sometimes realized the difficulty involved in the 
compatibility of all single predicates. Thus he says : "It is yet unknown to 
men what is the reason of the inoompossibility of different things, or how it is 
that different essences can be opposed to each other, seeing that all purely 
positive terms seem to be compatible " inter se (G. vii. 195 ; quoted by Caird, 
Critical Philosophy of Kant, i. pp. 93—4). (The date is before 1686.) 



THE LAW OF CONTRADICTION. 21 

involves the incompatibility of its constituents with the pos- 
session of angles. But for this synthetic relation of incom- 
patibility, no negative proposition would occur, and therefore 
there could be no proposition involved which would be directly 
contradictory to the definition of a square. This is almost 
admitted by Leibniz, when he urges that truths are not 
arbitrary, as Hobbes supposed, because " notions are not always 
reconcilable among themselves" (D. 30; G. iv. 425). Since 
the possibility of God, as defined by Leibniz, depends upon the 
fact that all simple ideas are " reconcilable among themselves,'' 
and since all notions are composed of simple ideas, it is difficult 
to see how the two views are to be combined. Thus Leibniz's 
criterion of possible and impossible ideas can never apply to 
simple ideas, and moreover always presupposes those simple 
ideas and their relations — relations which can only be expressed 
in synthetic propositions. Two simple ideas can never be 
mutually contradictory in Leibniz's sense, since mere analysis 
will not reveal any further predicate possessed by the one and 
denied by the other. Thus a self-contradictory idea, if it be 
not a mere negative, such as a non-existent existent, must 
always involve a synthetic relation of incompatibility between 
two simple notions. The impossible idea, in Leibniz's sense, 
presupposes the idea which is impossible on account of some 
synthetic proposition ; and conversely, the possible complex 
idea is possible on account of a synthetic proposition asserting 
the compatibility of its simple constituents. Thus to return to 
Arithmetic, even if 2 -f- 1 be indeed the meaning of 3, still the 
proposition that 2-1-1 is possible is necessarily synthetic. A 
possible idea cannot, in the last analysis, be merely an idea 
which is not contradictory ; for the contradiction itself must 
always be deduced from synthetic propositions. And hence the 
propositions of Arithmetic, as Kant discovered, are one and all 
synthetic. 

In the case of Geometry, which Leibniz also regards as 
analytic, the opposite view is even more evidently correct. 
The triple number of dimensions, he says, follows analytically 
from the fact that only three mutually perpendicular lines can 
be drawn through one point (G. vi. 323). No instance, he 
says, could be more proper for illustrating a blind necessity 



22 THE LAW OF CONTRADICTION. 

independent of God's will. It is amazing that he did not 
perceive, in this instance, that the proposition from which the 
three dimensions are supposed to be deduced is in fact precisely 
the same as the three dimensions, and that, so far from being 
proved, it is wholly incapable of deduction from any other 
proposition, and about as synthetic as any proposition in the 
whole range of knowledge. This is so obvious as to need no 
further argument; and it is an interesting fact that Kant, in 
his first published work', points out the circularity of Leibniz's 
deduction in the above passage of the Thiodicde, and proceeds, 
being still a Leibnizian, to infer that the number of dimensions 
is synthetic and contingent, and might be different in other 
possible worlds (ed. Hartenstein, 1867, i. p. 21 ff.). 

We may argue generally, from the mere statement of the 
Law of Contradiction, that no proposition can follow from 
it alone, except the proposition that there is truth, or that 
some proposition is true. For the law states simply that any 
proposition must be true or false, but cannot be both. It gives 
no indication as to the alternative to be chosen, and cannot of 
itself decide that any proposition is true. It cannot even, of 
itself, yield the conclusion that such and such a proposition is 
true or false, for this involves the premiss " such and such is a 
proposition," which does not follow from the law of contra- 
diction. . Thus the doctrine of analytic propositions seems 
wholly mistaken. 

It may be worth pointing out that even those propositions 
which, at the beginning of the enquiry, we took as the type of 
analytic propositions, such as "the equilateral rectangle is a 
rectangle," are not wholly analytic. We have already seen 
that they are logically subsequent to synthetic propositions 
asserting that the constituents of the subject are compatible. 
They cannot, therefore, in any case, give the premisses of any 
science, as Leibniz supposed (cf. N. E. p. 99 ; G. v. 92). But 
further, in so far as they are significant, they are judgments of 
whole and part ; the constituents, in the subject, have a certain 
kind of unity — the kind always involved in numeration, or in 
assertions of a whole — which is taken away by analysis. Thus 
even here, in so far as the subject is one, the judgment does not 
1 Gedanken von der wahren Schdtzung der lebendigen Krafte, 1747. 



THE LAW OF CONTRADICTION. 23 

follow from the Law of Contradiction alone. And iri the closely 
allied judgments, such as "red is a colour," " 2 is a number," 
"number is a concept," the subject is not even complex, and 
the proposition is therefore in no sense analytic. But this last 
assertion is one which I cannot here undertake to prove. 

12. As regards the second point which was to be discussed, 
namely the connection of the necessary and the analytic, it is 
evident, from what has been said already, that if there are to 
be any necessary propositions at all there must be necessary 
synthetic propositions. It remains to enquire what we mean" 
by necessity, and what distinction, if any, can be made between 
the necessary and the contingent. 

Necessity itself is never discussed by Leibniz. He dis- ' 
tinguishes kinds of necessity- — metaphysical, hypothetical, and 
moral — but he nowhere explains metaphysical necessity, which 
is here in question, otherwise than as the property of analytic 
propositions. Nevertheless, necessity must mean something 
other than connection with the Law of Contradiction; the 
statement that^nalytic propositions are necessary is-significant, 
and the opposite statement — that synthetic propositions are 

contingent-rris certaialy so regarded by Leibniz,. It_:sM)JiUL 

seeni-ihat-ngcessity is ultimate and indefinable. We may say, 
if we choose, that a necessary proposition is one whose contra- 
dictory^impossible ; but the impossi15Ie~can only be defi^iied 
by means^~the iiecessary, so that this account would give no 
information as to necessity. In holding necessa£y^propositions 
to be analytic , Leibniz ^agr eeowith all his predecessors, and 
witiTthose of his successors who_preceded IplHt; But by the 
discoveryThat the laws of motion are synthetic, and by his 
strict determinism, he rendered the denial of necessary syn- 
thetic propositions highly paradoxical in its consequences, and 
prepared the way for Kant's opposite assertion. (For Leibniz, 
by the way, the necessary is not, as for Kant, the same as the 
dL_ priori-, we shairfind~ffiat contingent propositions als6~have 
a priori proofs. The^TjHorrisrSTF^antrwtat^s indepen- 
dent of .particular experience, buTTthe^n'ecessary is not co- 
extensive with this.) Leibd.z.,and„Kant both held th at^there 
is a fundamental distinction between propositions that are 
necessarj, and thosejhat are contingent, or, in Kant's language. 



24 THE LAW OF CONTRADICTION. 

empirical. Thus the propositions of mathematics are necessary, 
while those- assertiQgjparticular existence are contingent;^ It 
may be questioned whether this distinction is lenahle, whether, 
in fact, there is any sense in saying, of a true proposition, that 
it might have been false. As long as the distinction of analytic 
and synthetic propositions subsisted, there was some plausibility 
in maintaining a corresponding distinction in respect of ne- 
cessity. But Kant, by pointing out jthat^ maihematical judg- 
ments are both necessary and synthetic, pr&pared- the jyay:^for 
the view^hat this is true of all judgments^_,^ The distinction of 
the , empirical and the a priori seems to depend upon con- 
founding sources of knowledge with grounds of truth, i There 
is no doubt a great difference between knowledge gained by 
perception, and knowledge gained by reasoning ; but ttat does 
not show a corresponding difference as to what is known. The 
further discussion of this point, however, must be postponed 
till we come to Leibniz's theory of perception. And it must be 
confessed that, if all proposition's are necessary, the notion of 
necessity is shorn of most of its importance. 

Whatever view we adopt, however, aa regards the necessity 
of existential propositions] it must be admitted that arith- 
metical propositions are'both necessary and syntheticv an'd~t1iis 
is enough tojdestroy the supposed connecfton of the necessary 
and the analytic. 

In tEe~next Chapter we shall have a less destructive task.) 
We shall have to show the true principle and the true import- 
ance of Leibniz's division of propositions into two kinds, and 
the meaning of the Law of Sufficient Reason, which he invoked 
as the source of his contingent propositions. 



CHAPTER III. 



CONTINGENT PROPOSITIONS AND THE LAW OF SUFFICIENT 

EEASON. 

13. We have now seen that Leibniz's division of propositions 
into two classes, in the form in which he gave it, is untenable. 
Necessary propositions are not to be defined as those that 
follow from the Law of Contradiction ; and as regards proposi- 
tions which are not necessary, it may be questioned whether 
any such are to be found. ^ Nevertheless, there is a most 
important principle by which propositions may be divided into 
tvyp classes. This principle, we shall find, leads to the same 
division of propositions as that to which Leibniz was led, and 
may, by examination of his words, be shown to be the true 
principle upon which his division proceeded. His division 
does, therefore, correspond to what is perhaps the most im- 
portant classification of which propositions are capable. I 
shall first explain this classification, and then examine the 
Law of Sufficient Reason, which Leibniz held to be the 
supreme principle of contingent propositions. 

Contingent propositions, in Leibniz's system, are, speaking 
generally, such as assert actual existence. The exception 
which this statement requires, in the case of the necessary 
existence of God, may be provided for by saying that contin- 
gent propositions are such as involve a reference to parts of 
time.) This seems to be Leibniz's meaning when he says 
(G. III. 588) : " The notion of eternity in God is quite different 
from that of time, for it consists in necessity, and that of time 



26 THE LAW OF SUFFICIENT REASON. 

in contingency." Thus necessary propositions are such as have 
no reference to actual time, or such as — except in the case of 
God — do not assert the existence of their subjects. " As for 
the eternal truths," Leibniz says, "we must observe that at 
bottom they are all conditional, and say in fact : Such a 
thing posited, such another thing is" (N. E. p. 515; G. V. 
428). And again: "Philosophers, who distinguish so often 
between what belongs to essence and what to existence, refer 
to existence all that is accidental or contingent " (N. E. p. 498 ; 
G. V. p. 414). He points out also that the truth of a necessary 
proposition does not depend upon the existence of its subject 
(N. E. p. 516 ; G. v. 429). The designation as eternal truths, 
which he always adopts, must be meant to indicate that no 
special time is referred to in the proposition ; for the proposi- 
tion itself, of whatever nature, must of course be eternally 
true or eternally false. 

But propositions about contingency itself, and all that can 
be said generally about the nature of possible contingents, are 
not contingent; on the contrary, if the contingent be what 
actually exists, any proposition about what might exist must 
be necessary. Thus Leibniz says (G. i[. 39): "The notion of a 
species involves only eternal or necessary truths, but the notion 
of an individual involves, sub ratione possibilitatis, what is of 
fact, or related to the existence of things and to time." He 
proceeds to explain that the notion of the sphere which Archi- 
medes caused to be placed on his tomb involves, besides its 
form, the matter of which it was made, as well as the place and 
time. This passage is very important, for it involves the dis- 
tinction, afterwards urged by Kant against the ontological 
argument, between the notion of an existent and the assertion 
of actual existence. (The notion of an individual, as Leibniz 
puts it, involves reference to existence and time sicb ratione 
possibilitatis, i.e. the notion is exactly what it would be if the 
individual existed, but the existence is merely possible, and is 
not, in the mere notion, judged to be actual.] " Possibles are 
possible," he says, "before all actual decrees of God, but not 
without sometimes supposing the same decrees taken as possi- 
ble. For the possibilities of individuals or of contingent truths 
contain in their notion the possibility of their causes, to wit, 



THE LAW OF SUFFICIENT REASON. 27 

the free decrees of God ; in which they are different from the 
possibilities of species or eternal truths, which depend only 
upon the understanding of God, without involving his will" 
(G. II. 51). That is to say, possible existents involve possible 
causes, and the connection between a possible cause and a 
possible effect is similar to that between an actual cause and 
an actual effect. But s_o„long^sjs^do_nQt_aaaert actual exist- 
ence. we are still in the region of eternal truths, and although, 
as we shall see, the law of sufficient reason does apply to 
possibles, still it is not, in such applications, coordinate with 
the principle of contradiction, but only a consequence of that 
principle. <^It is in taking the further step, iu judging the 
actual existence of the individual whose notion is in question, 
that the law of sufficient reason becomes indispensable, and 
gives results to which the law of contradiction is, by itself, 
inadequate^? The individual once posited, all its properties 
follow : " every predicate, necessary or contingent, past, present, 
or future, is comprised in the notion of the subject " (G. ii. 46). 
But it does not follow that this notion represents a subject 
which exists : it is merely the idea of a subject having the 
general qualities distinguishing existents. ^Existence is thus 
unique among predicates. All other predicates are contained 
in the notion of the subject, and may be asserted of it in a 
purely analytic judgment.^ The asserjjon of existence, alone 
among predicates, is synthetic, and therefore, in Leibniz's view, ,1 
contingent. Thus existence has, for him, just as peculiar a 
position as it has in Kant's criticism of the ontological proof, 
and it must be regarded as a sheer inconsequence, in Leibniz, 
that he failed to apply his doctrine also to God. But for the ^ 
fact that Leibniz definitely asserts the^"contrary (N. E. 401 ; 
G. V. 339)', one would be tempted to state his position as 
tantamount to a denial that existence is a predicate at all. 

But further, not only the existence of such and such a 
subject is contingent, but also the connection of any two predi- 
cates expressing the states of that subject at different times. 
Thus Leibniz says, in discussing the supposition that he is 

1 "When we say that a thing exists, or has real existence, this existence 
itself is the predicate, i.e. it has a notion joined to the idea in question, and 
there is connection between these two notions." 



-\ 



28 THE LAW OF SUFFICIENT REASON. 

going, at some future time, to make a journey, " the connection 
of events, though certain, is not necessary, and it is open to me 
to make or not to make this journey, for though it is included 
in my notion that I shall make it, it is also included in it that 
I shall make it freely. And there is nothing in me, of all that 
can be conceived generally, or by essence, or by a specific or 
incomplete notion, whence it can be concluded that I shall 
do so necessarily, whereas from my being a man it can be 
concluded that I am capable of thinking; and consequently, 
if I do not make this journey, that will not combat any eternal 
or necessary truth. Nevertheless, since it is certain that I . 
shall do so, there must be some connection between me, who 
am the subject, and the execution of the journey, which is the 
predicate ; for, in a true proposition, the notion of the predicate 
is always in the subject. Consequently, if I did not do so, 
there would be a falsity, which would destroy my individual or 
complete notion " (G. il. 52). Thus those predicates which are 
concretes, i.e. those expressing states of a substance at par- 
ticular parts of time, are in a different position from such 
abstract predicates as human and rational. Concrete predi- 
cates, though they are connected with each other, are not 
necessarily connected; the connections, as well as the predi- 
cates, are contingent. All the predicates are necessarily con- 
nected with the subject, but no concrete predicates are neces- 
sarily connected with each other. And hence Leibniz often 
speaks of them as contingent predicates. If the series of 
predicates were different, the subject would be different ; hence 
the necessary connection of predicates and subject amounts to 
little more than the law of identity'. A subject is defined by 
its predicates, and therefore, if the predicates were different, 
the subject could not be the same. Thus it follows, from a 
subject's being the subject it is, that it will have all the predi- 
cates that it will have; but from one or more of its predicates, 
this does not follow necessarily. The existence of each separate 
predicate at each separate instant is a contingent truth, for 
each is presupposed in the assertion that just such a subject 
exists. ''There is a difficulty, on this view, in distinguishing 

1 "It would not have been our Adam, but another, if he had had other 
events" (G. n. 42). 



THE LAW OF SUFFICIENT REASON. 29 

a subject from the sum of its predicates— a difficulty to which 
I shall return when I. come to the doctrine of substance. For 
the present, I am content to point out that, in asserting the 
existence of an individual substance, i.e. of a subject whose 
notion is complete, there are involved just as many separate 
contingent propositions as there are moments through which 
the substanoe persjsts. For the state of the substance at each 
moment exists, and its existence is a contingent proposition. 
It is thus existential propositions that are contingent, and pro- 
positions not asserting existence that are necessary. Leibniz's 
division of propositions into two kinds does, therefore, corre- 
spond to a very important division — perhaps the most im- 
portant — of which propositions are susceptible. 

Some explanation seems, however, to be called for by the 
connections of contingent predicates. These connections can 
hardly be said to exist, and yet they are always contingent, not 
only in free substances, but also in such as have no freedom. 
In substances which are not free, the connections of successive 
states are given by the laws of motion, and these laws are most 
emphatically contingent. Leibniz even goes so far as to say < 
that it is in Dynamics that we learn the distinction of necessary 
and contingent propositions (G. III. 645). Besides these, there 
is the general law, equally contingent, but equally without 
exception, " that man will always do, though freely, what seems 
the best" (G. iv. 4.38). The fact seems to be, that these 
general but not necessary laws are regarded by Leibniz as 
essentially referring to every part of actual time. That is to 
say, they do not hold of the sequences in other possible time- 
orders, but only of actual sequences.]? Moreover they are 
deduced from elements in the actual preceding state, which 
elements lead to the sequence, and are logically prior to it — 
this is, as we shall see, essential to the doctrine of activity. 
Thus these laws, though they have an a priori proof by means 
of final causes, are yet of the nature of empirical generalisations. 
They have held, they hold now, and they, will hold hereafter. 
They apply to every moment of actual time, but they cannot 
be stated without such reference. This is a conception which 
I shall have to criticize when we come to deal with Leibniz's 
philosophy of Dynamics. For the present, I only wish to point 



30 THE LAW OF SUFFICIENT REASON. 

out that, in his system, the laws of motion and the law of 
volition are existential, and do have an essential reference to 
the parts of actual time. They are peculiar only in referring 
to all parts of time. They may be contrasted, in this respect, 
with the properties of time itself, which are metaphysically 
necessary, and the same in all possible worlds; whereas the 
emstence of time is contingent, since it depends upon God's free 
resolve to create a world. 

Leibniz's dichotomy of propositions amounts, therefore, to 
the following assertions. All true propositions not involving 
actual existence, but referring only to essences or possibles, are 
necessary ; but propositions asserting existence — except in the 
case of God — are never necessary, and do not follow necessarily 
from any other existential proposition, nor yet from the fact 
-that the subject has all the qualities distinguishing existents'. 
If, then, existential propositions are to have any interrelations, 
and are to be in any way systematized, there must be some 
principle by which their merely particular and contingent 
character is mitigated. 

14. This brings me to the principle of sufficient reason. 
This principle is usually supposed to be, by itself, adequate 
to the deduction of what actually exists. To this supposi- 
tion, it must be confessed, Leibniz's words often lend colour. 
But we shall find that there are really two principles included 
under the same name, the one general, and applying to all 
possible worlds, the other specjal, and applying only to the 
actual world. (Both differ from the law of contradiction, by 
the fact that they apply specially — the former, however, not 
exclusively — to existents, possible or actual.) The former, as we 
shall see, is a form of the law of causality, asserting all possible 
causes to be desires or appetites; the latter, on the other hand, 
is the assertion that all actual causation is determined by 
desire for the good. The former we shall find to be meta- 
physically necessary, while the latter is contingent, and applies 
only to contingents. The former is a principle of possible 
contingents, the latter a principle of actual contingents only. 
The importance of this distinction will appear as soon as we 

' On the connection of contingency with infinite complexity (which many 
commentators regard as defining contingency) see Chap. V. § 26. 



THE LAW OF SUFFICIENT REASON. 31 

begin to examine Leibniz's accounts of what he means by 
sufiScient reason'. 

The law of sufficient reason is variously stated by Leibniz 
at various times. I shall begin with his later statements, 
which are better known, and more in accordance with the 
traditional view of its import ; I shall then refer to the earlier 
statements, especially those of 1686, and examine whether 
these can be reconciled with the later forms of the principle. 

The statement in the Monadology is as follows (§§ 31, 32, 
33, 36) : " Our reasonings are founded upon two great princi- 
ples, that of contradiction, and that of sufficient reason, 

in virtue of which we judge that no fact can be found true or 
exist ent, no statement veritable, unle ss there is a sufficient reas on 
why it should be so and not otherwise, although these reasons 
usually cannot be known to us. There are also two kinds of 
truths, those of reasoning, and those of fact. Truths of reason- 
ing are necessary, and their opposite is impossible ; truths of 
fact are contingent, and their opposite is possible. When a 

truth is necessary, the reason of it can be found by analysis 

But there must also be a sufficient reason for contingent truths 
or truths of fact, i.e. for the sequence of things which are 
dispersed throughout the universe of created beings, in which 
the resolution into particular reasons might go on into endless 
detail " (D. 222—3 ; L. 235—7 ; G. vi. 612). (This leaves us 
entirely uninformed as to what is meant by a sufficient reason. 
The same vagueness appears in the Principles of Nature and 
of Grace (§7): "Thus far we have spoken only as mere physi- 
cists : now we must rise to metaphysics, by making use of the 
great principle, little employed in general, which affirms that 
nothing happens without a sufficient reason; i.e. that nothing 
happens without its being possible for one who should know 
things sufficiently to give a reason sufficient to determine why 
things are so and not otherwise. This principle being laid 
down, the first question we are entitled to put will be, why 
is there something rather than nothing ? For nothing is simpler 
and easier than something. Further, supposing that things 

' I do not maintain that Leibniz himself was perfectly clear as to these two 
principles of sufficient reason, but that he did, as a matter of fact, designate 
two distinct principles (perhaps not distinguished by him) by this same name. 



32 THE LAW OF SUFFICIENT REASON. 

must exist, we must be able to give a reason why they must 
exist thus and not otherwise " (D. 212—3 ; L. 414 — 5 ; G. vi. 
602). This statement, though it brings out very clearly the 
connection of contingency and existence, gives us no further 
information as to the meaning of sufficient reason. In the 
paper " On the Ultimate Origination of Things" (1697) Leibniz 
is a little more definite. He says: "In eternal things, even 
though there be no cause, there must be a reason, which, for 
permanent things, is necessity itself, or essence; but for the 
series of changing things, if it be suppo.sed that they succeed 
one another from all eternity, this reason is, as we shall 
presently see, the prevailing of inclinations, which consist not 
in necessitating reasons, i.e. reasons of -aji absolute and meta- 
physical necessity, the opposite of which involves a contra- 
diction, but in inchning reasons" (L. 338 ; D. 100 ; G. vii. 302). 
What is meant by thesS' inclining reasons cannot be properly 
explained until we come to deal with the activity of substance. ) 
In dealing with actual existents, the inclining reason is the 
perception of the good, either by the substance itself, if it be 
free, or by God, if the substance be not free. But the law as 
above stated, even in the form which applies only to the series 
of changing things, is true, as we shall soon see, not only of the 
actual world, but of all possible worlds. It is, therefore, itself 
metaphysically necessary, and unable to distinguish the actual 
from the possible. Even in the form which applies only to the 
series of changing things, the law is still a law of all possible 
contingents; and any true proposition about possible contin- 
gents must itself be not contingent, but necessary. 

Before developing this topic, let us examine Leibniz's earlier 
statements of the law. In the year 1686, when he was more 
incljped than in later years to go to the bottoin of his principles, 
he gives a statement at first sight very different from those 
which he usually gives, and refers to his usual formula as a 
" vulgar axiom " which follows as a corollary. He says : " There 
must always be some foundation of the connection of terms in a 
proposition, which must be found in their notions. This is my 
great principle, with which I believe all philosophers must 
agree, and of which one of the corollaries is this vulgar axiom, 
that nothing happens without a reason... though often this 



THE LAW OF SUFFICIENT REASON. 33 

reason inclines without necessitating" (G. ii. 56). And again 
he says that in Metaphysics he presupposes hardly anything 
but two great principles, namely (1) the law of contradiction, 
and (2) " that nothing is without a reason, or that every truth 
has its d priori proof, drawn from the notion of the terms, 
although it is not always in our power to make this analysis " 
(G. II. 62). 

There is another passage, in an undated paper, which how- 
ever, on internal evidence, would seem to belong to the same 
period, in which Leibniz is even more definite on the d priori 
proof of contingent propositions. " Generally, every true propo- 
sition," he says, " (which is not identical or true per se) can be 
proved d priori by the help of axioms, or propositions true per 
se, and by the help of definitions or ideas. For as often as a 
predicate is truly affirmed of a subject, some real connection is 
always judged to hold between the predicate and the subject, 
and thus in any proposition : A is B (or, B is truly predicated 
of A), B is always in A itself, or its notion is in some way con- 
tained in the notion of A itself; and this either with absolute 
necessity, in propositions of eternal truth, or with a kind of 
certainty, depending upon a supposed decree of a iree substance, 
in contingent things ; and this decree is never wholly arbitrary 
and destitute of foundation, but always some reason for it 
(which however inclines, and does not necessitate), can be given, 
which could itself be deduced from analysis of the notions (if 
this were always within human power), and certainly does not 
escape the omniscient substance, which sees everything d priori 
by means of ideas themselves and its own decrees. It is certain, 
therefore, that all truths, even the most contingent, have an 
d priori proof, or some reason why they are rather than are not. 
And this is itself what people commonly say, that nothing 
happens without a cause, or that nothing is without a reason." 
(G. VII. 300, 301)'. 

1 The principle of sufficient reason, in bo far as it is independent of final 
causes, occurs in Spinoza (Ethics, i. 11, 2nd dem.) : " For the existence or non- 
existence of anything, it must be possible to assign a cause or reason." Leibniz 
was aware of this agreement, as appears from the following comment on 
SchuUer's account of Spinoza : " This is rightly observed, and agrees with what 
I am wont to say, that nothing exists unless a sufficient reason of its existence 
can be given, which is easily shown not to lie in the series of causes." [G. 1. 138.] 

B. L. 3 



34 THE LAW OF SUFFICIENT EEASON. 

These statements, as they stand, seem different from 
Leibniz's later statements of the law of sufficient reason. But 
it would seem that he intends, in contingent matter, to include, 
in " the notion of the terms," the pursuit of the apparently best. 
This appears quite plainly in a passage also written in 1686, 
where he says that the actions of Caesar, though contained in 
his notion, depend upon God's free choice to create men, and to 
make them such that they would always choose, though freely, 
what seemed best to them. It is only thus, he says, that such 
predicates can be shown d priori to belong to Caesar (G. IV. 
438). 

Thus the law of sufficient reason, as applied to actual 
existents, reduces itself definitely to the assertion of finj.1 
causes, in the sense that actual desires are always directed 
towards what appears the best. In all actual changes, the con- 
sequent can only be deduced from the antecedent by using the 
notion of the good. Where the change depends only upon God, 
it really is for the best ; where it depends upon a free creature, 
it is such as seems best to the creature, but is often, owing to 
confused perception, not really the best possible change. Such 
a connection can only be regarded as contingent by admitting, 
as Leibniz does, that a law may be general, i.e. may apply to 
every part of time, without being necessary, i.e. without being 
capable of a statement in which no actual part of time is 
referred to.) To pursue this topic is impossible until we come 
to the doctrine of substance. At present I will only point 
out that this principle confers upon the good a relation to 
existence such as no other concept possesses. In order to infer 
actual existence, whether from another existent, or from mere 
notions, the notion of the good must always be employed. It 
is in this sense that contingent propositions have a priori 
proofs^. "As possibility is the principle of essence," Leibniz 
says, ■' so perfection, or a degree of essence (by which the 
greatest number of things are compossible), is the principle 

1 The a priori, in Leibniz, is opposed to the empirical, not to the contingent. 
A proof employing the notion of the good may show, without appealing to 
experience, that something exists, but does not thereby render this proposition 
necessary. Thus the a priori is not, as in Kant, synonypaous with the 
necessary. 



THE LAW OF SUFFICIENT REASON. 35 

of existence " (D. 103 ; L. 342—3 ; G. vii. 304)i. This con- 
nection of existence with the good, the principle that all actual 
causation is determined by desire for what appears best, is a 
most important proposition, which we shall have to consider 
again at a later stage. It gives the essence of the law of 
sufficient reason as applied to actual existents. (At the same 
time we shall see that the law has also a wider meaning, in 
which it applies to possible existents as well. The confusion 
of these two has rendered the connection of the law with the 
principle of contradiction very difficult to understand. The 
distinction will, I think, enable us to clear up the connection 
of Leibniz's two principles.) 

15. When we enquire into the relation of the law of suffi- 
cient reagon to the law of contradiction, we find that Leibniz 
makes very few remarks on the subject, and that those few 
give a meaning to the law of sufficient reason, in which it 
applies equally to all possible worlds. We then require a 
further principle, applicable only to the actual world, from 
which actual existence may be inferred. T his is to befoiind in 
fin al cause s. But let us see what Leibniz says. 

"I certainly maintain," he writes to Des Bosses, "that a 
power of determining oneself without any cause, or without any 
source of determination, implies contradiction, as does a relation 
without foundation ; but from this the metaphysical necessity 
of all efifects does not follow. For it suffices that the cause or 
reason be not one that metaphysically necessitates, though it is 
metaphysically necessary that there should be some such cause " 
(G. II. 420). In this passage he is evidently thinking of the 
volitions of free creatures ; in a letter to the Princess of Wales, 
accompanying the fourth paper against Clarke, he makes the 
same statement concerning God. " God himself," he says, 
" could not choose without having a reason of his choice " 
(G. VII. 379). But we know that God, being free, might have 
chosen otherwise, and therefore, since he must have a reason 
for his choice, there must have been possible reasons for possible 

1 Perfection here has its metaphysical sense, as the "amount of positive 
reality" (Monadology , § 41, D. 224), but Leibniz certainly thought metaphysical 
perfection good. In the sentence preceding the one quoted in the text, he speaks 
of "imperfection or moral absurdity" as synonymous, and means by imper- 
fection the opposite of metaphysical perfection. See Chap. xvi. 

3—2 



36 THE LAW OF SUFFICIENT REASON. 

choices, as well as actual reasons for actual choices. The same 
consequence follows as regards free creatures. And this conse- 
quence, as appears from a passage quoted above (G. II. 51 ; § 13), 
was actually drawn by Leibniz. In order that a notion may be 
the notion of a possible existent, there must be another notion 
which, if it existed, would be a sufficient reason for such an 
imagined existent. "There were," Leibniz continues, "an 
infinity of possible ways of creating the world, according to 
the different designs which God might form, and each possible 
world depends upon certain principal designs or ends of God 
proper to itself" (G. il. 51). 

But if the principle applies to possible as well as actual 
existents, how is it to help in determining what does actually 
exist ? It gives merely, on this view, a general quality of what 
might exist, not a source of actual existents'. This Leibniz 
would admit. And we may now clearly state the distinction 
between actual and possible sufficient reasons. The part of the 
principle which is metaphysically necessary, which applies 
equally to possible and to actual existents, is the part which 
asserts all events to be due to design. From the passage at 
the end of the preceding paragraph, it appears that, whichever 
of the possible worlds God had created, he would always 
necessarily have had some design in doing so, though his 
design might not have been the best possible. And similarly 
volition, in free creatures, must have a motive, i.e. must be 
determined by some prevision of the effect. The relation of 
cause and effect can never be a purely external one ; the cause 
must be always, in part, a desire for the effect. This form of 
causality is the essence of activity, which Leibniz, as we shall 
see, declares to be metaphysically necessary to substance. And 
in this form, the law of sufficient reason is necessary and 
analytic, not a principle coordinate with that of contradiction, 
but a mere consequence of it. 

The principle which applies only to actuals, which is really 
coordinate with the law of contradiction, and gives the source 

' Of. G. II. 225 : De Voider objects to Leibniz that to conceive the existence 
of a substance we require a cause, but not to conceive its essence. ' ' I retort," 
Leibniz replies, " to conceive its essence we require the conception of a possible 
cause, to conceive its existence we require the conception of an actual cause." 



THE LAW OF SUFFICIENT REASON. 37 

of the world which does exist, is the principle that designs are 
always determined by the idea of the good or the best. God 
might have desired any of the possible worlds, and his desire 
would have been a sufficient reason for its creation. But it is 
a contingent fact that he desired the best, that the actual 
sufficient reason of creation was the desire for the maximum of 
good, and not for anything that the other possible worlds would 
have realised. So Leibniz says : " It is reasonable and assured 
that God will always do the best, though what is less perfect 
does not imply contradiction " (G. iv. 438)'. The same holds 
of free creatures, with the limitation that they are often mis- 
taken about the good. It would be possible to desire what 
does not appear best, but it is a contingent fact that actual 
desires, which are actual sufficient reasons, are always directed 
to what the free spirit holds to be the best possible'. It might 
be supposed that, if God is necessarily good, his acts also must 
necessarily be determined by the motive of the best. But this 
Leibniz evades by the common notion that freedom is essential 
to goodness, that God is good only because the evil which he 
■rejects IS possible — a notion which this is not the place to diseass. 
We may now sum up the results of our discussion of con- 
tingency and sufficient reason. Leibniz, holding fast to the 
doctrine that a necessary proposition must be analytic, dis- 
covered that existential propositions are synthetic, and also, like 
Hume and Kant, that all causal connections among existents 
differin g in temporal position are synth etic. He inferred, 
accordingly, that the actual world does not exist necessarily, 
and that, within this world, causes do not produce their effects 

' Of. G. vn. 309, text and note. Also the following passages in the fifth paper 
against Clarke [G. vii.] : No. 9 : "But to say, that God can only choose what is 
best ; and to infer from thence, that what he does not choose, is impossible ; 
this, I say, is confounding of terms : 'tis blending power and will, metaphysical 
necessity and moral necessity, essences and existences. For what is necessary, 
is so by its essence, since the opposite implies a contradiction ; but a contingent 
which exists, owes its existence to the principle of what is best, which is a 
sufficient reason of things." No. 73 : "God can do everything that is possible, 
but he will do only what is best." Cf. also No. 76. 

^ This appears also from a passage [G. ii. 40] where Leibniz explains that 
the present state of the world follows from the first state only in virtue of 
certain laws freely decreed by God. These laws, therefore, among which is the 
pursuit of the best, must be contingent. 



38 THE LAW OF SUFFICIENT REASON. 

necessarily. The reason, as he perpetually repeats, inclines 

2.,^ without necessitating. This was his solution of the problem 

/raised by the fact, which he perceived as clearly as Hume and 

( Kant, that causal connections are synthetic. Hume inferred 

that causal connections do not really connect, Kant inferred 

that the synthetic may be necessary, (Leibniz inferred that a 

connection may be invariable without being necessary ."> As he 

never dreamt of denying that the necessary must be analytic, 

this was his only possible escape from a total denial of causal 

connections. 

Thus the proposition that anything except God exists is 
contingent, and so is the proposition that one existent is the 
cause of another. At the same time, causality itself is necessary, 
and holds in all possible worlds. (^In all possible worlds, moreover, 
causality can only be rendered intelligible by regarding the 
cause as being in part a prevision or desire of the effect.^ This 
follows, as we shall see in the next chapter, from the general 
doctrine that "every extrinsic denomination has an intrinsic 
one for its foundation " (G. ii. 240), i.e. that no - relation is 
purely external. So far as this is asserted by the law of sufiS- 
cient reason, that law is metaphysically necessary. The effect 
must be the end in the psychological sense, i.e. the object of 
desire. But in the actual world, owing to God's goodness, the 
effect also is, or seems to be, the end in the ethical sense. The 
psychological end is, as a matter of fact, what the agent 
believes to be the ethical end, i.e. what he believes to be the 
best possible effect. (In substances which are not free, the 
sufficient reason does not lie in them, but in God.) This is 
what distinguishes the actual from any other possible world. 
God might have created one of the possible worlds,' but he 
could not have been ignorant of its not being the best. For its 
degree of excellence is an eternal truth, and an object of his 
understanding. But we are told (G. ii. 51) that whatever 
world God had created, he would have had a design in so doing, 
and that some design is metaphysically necessary to his acts- 
It only remains, therefore, to interpret design psychologically, 
not ethically, when design is said to be necessary. 

God's good actions then are contingent, and true only within 
the actual world. They are the source, from which all explana- 



THE LAW OF SUFFICIENT REASON". 39 

tion of contingents by means of sufiScient reason proceeds. 
They themselves, however, have their sufficient reason in God's 
goodness, which one must suppose metaphysically necessary^. 
Leibniz failed to show why, since this is so, God's good actions 
are not also necessary. But if they were necessary, the whole 
series of their consequences would have been also necessary, 
and his philosophy would have fallen into Spinozism. The 
only remedy, would have been, to declare God's existence, like 
all other existence, contingent — a remedy irresistibly suggested 
by his logic, but regarded by him, for obvious reasons, as worse 
than the disease of Spinozism which his doctrine of contingency 
was designed to cure. 

' Leibniz nowhere, so far as I know, definitely asserts God's goodness to be 
necessary, but this oonolusion seems to follow from his philosophy. For God's 
goodness is an eternal truth, not referring solely, as do his acts, to the actual 
world. We can hardly suppose that, in other possible worlds, God would not 
have been good, or that it is a merely contingent fact that God is good. But if 
we were to make this supposition, we should merely remove the difficulty one 
stage further, since we should then require a sufficient reason for God's good- 
ness. If this reason were necessary, God's goodness would also be necessary ; 
if contingent, it would itself require a sufficient reason, concerning which the" 
same difficulty would recur. 



40 



CHAPTER IV. 



THE CONCEPTION OF SUBSTANCE. 

16. The question to be discussed in this chapter is : What 
did Leibniz mean bj- the word substance, arid how far can this 
meaning be fruitfully employed in philosophy ? This question 
must be carefully distinguished from the question which is 
answered by the doctrine of Monads, namely, what existential 
judgments can we make, in which the notion of substance is 
employed ? Our present question is simply, what is the notion 
of substance? Not, what judgments about the world can be 
made by the help of this notion ? 

The conception of substance dominated the Cartesian philo- 
sophy, and was no less important in the philosophy of Leibniz. 
But the meaning which Leibniz attached to the word was 
different from that which his predecessors had attached to it, 
and this change of meaning was one of the main sources of 
novelty in his philosophy. Leibniz himself emphasized the 
importance of this conception in his system. As against Locke, 
he urged that the idea of substance is not so obscure as that 
philosopher thought it (N. E. 148 ; G. v. 133). The considera- 
tion of it, he says, is one of the most important and fruitful 
points in philosophy : from his notion of substance follow the 
most fundamental truths, even those concerning God and souls 
and bodies (D. 69; G. iv. 469). To explain this notion is, 
therefore, an indispensable preliminary to a discussion of his 
views on matter or of his theory of Monads. 
I The Cartesians had defined substance as that which needs, 
, for its existence, only God's concurrence. By this they meant, 
practically, that its existence was not dependent upon relations 
to any other existents ; for God's concurrence was an awkward 



THE CONCEPTION OF SUBSTANCE. 41 

condition, which had led Des Cartes to affirm that ,God alone 
was properly and strictly a substance. Thus although, practi- 
cally, they admitted two substances, mind and matter, yet, 
whenever they took God seriously, they were compelled to deny 
the substantiality of everything except God. This inconsistency | 
was remedied by Spinoza, to whom substance was causa sui, I 
the self-caused, or that which is in itself and is conceived 
through itself. Substance to him, was therefore God alone — a 
remedy which Leibniz regarded as condemning the original 
definition (G. VI. 582). To Spinoza, extension and thought did 
not constitute separate substances, but attributes of the one 
substance. In Spinoza as in Des Cartes, the notion of sub- 
stance, though not by them clearly analyzed into its elements, 
was not an ultimate simple notion, but a notion dependent, in 
some undefined manner, upon the purely logical notion of 
subject and predicate. The attributes of a substance are the 
predicates of a subject ; and it is supposed that predicates 
cannot exist without their subject, though the subject can 
exist without them. -Hence the subject becomes that whose 
existence does not depend upon any other existent. 

There is an interesting discussion of this definition, in 
connection with Malebranche, in the Dialogue between Phila- 
rete and Ariste (G. VI. pp. 579 — 594). In this dialogue, the 
representative of Malebranche begins by defining substance as 
whatever can be conceived alone, or as existing independently 
of other things (G. vi. 581). Leibniz points out, in objection, 
that this definition, at bottom, applies only to God. " Shall we 
then say," he proceeds, " with an innovator who is but too well- 
known, that God is the only substance, and creatures are mere 
modifications of him ? " If the independence is to extend only 
to created things, then, Leibniz thinks, force and life, abstractly 
at least, can be so conceived. Independence in conception, he 
says, belongs not only to substance, but also to what is essential 
to substance. Malebranche's supporter then confines his defini- 
tion to concretes : substance is a concrete independent of every 
other created concrete. To this Leibniz retorts (1) that the 
concrete can perhaps only be defined by means of substance, so 
that the definition may involve a vicious circle'; (2) that 
* This objection however is subaequently withdrawn (16. 583). 



42 THE CONCEPTION OF SUBSTANCE. 

extension is not a concrete, but the abstract of the extended, 
which is the subject of extension (lb. 582). But he avoids, in 
this place, any definition of his own, contenting himself, in a 
characteristically conciliatory manner, with pointing out, that 
the above rectified definition will apply to Monads alone 
(lb. 585—6). 

17. Leibniz perceived, however, that the relation to subject 
and predicate was more fundamental than the doubtful infer- 
ence to independent existence (cf. G. il. 221). He, therefore, 
definitely brought his notion of substance into dependence upon 
this logical relation. He urges against Locke that there is 
good reason to assume substance, since we conceive several 
predicates in one and the same subject, and this is all that is 
meant by the words support or substratum, which Locke is using 
as synonymous with substance (N. E. p. 225 ; G. V. 201 — 2). 

■ But when we examine further, we find that this, though an 
essential part of the meaning of substance, is by no means all 
that this word means. Besides the logical notion of subject, 
there has been, as a rule, another element in the meaning 
people have attached to the word substance. This is the element 
of persistence through chan ge. Persistence is involved, indeed, 
in the very notion of change as opposed to mere becoming. 
Change implies something which changes ; it implies, that is, a 
subject which has preserved its identity while altering its quali- 
ties. <CThis notion of a subject of change is, therefore, not inde- 
pendent of subject and predicate, but subsequent to it ; it is 
the notion of subject and predicate appiie_d to what is in tinae."" 
It is this special form of the logical subject, combined with the 
doctrine that there are terms which can only be subjects and 
not predicates, which constitutes the notion of substance as 
Leibniz employs it. If we are to hold, he says, that I am the 
same person as I was, we must not be content with mere 
internal experience, but must have an d priori reason. This 
can only be that my present and past attributes are predicates 
of the same subject (G. II. 43).) The necessity of substance in 
the sense of a subject of change has been pointed out by Kant 
in the first analogy of experience. But to Kant, this subject is 
as phenomenal as its predicates. The distinctive feature of 
substance, when used as the basis of a dogmatic metaphysic, is 



THE CONCEPTION OF SUBSTANCE. 43 

the belief that certain terms are only and essentially subjects. 
When several predicates can be attributed to a subject, and 
this in turn cannot be attributed to any other subject, then, 
Leibniz says, we call the subject an individual substance (G. iv. 
432). This point is important ; for it is plain that any term 
may be made a subject. I may say " two is a number," " red is 
a colour," and so on. But such terms can be attributed to 
others, and therefore are not substances. The ultimate subject 
is always a substance (G. II. 457 — 8). Thus the term I appears 
incapable of attribution to any other term ; I have many predi- 
cates, but am not in turn a predicate of anything else. I, 
therefore, if the word I does denote anything distinct from the 
mere sum of my states, and if I persist through time, fulfil 
Leibniz's definition of a substance. *! Space, as Leibniz often 
admits, would, if it were real, which he denies, be a substance ; 
for it persists through time, and is not a predicate^. 

Substance, then, is that which can only be subject, not 
predicate, which has many predicates, and persists through 
change. It is, in short, the subject of change. The different 
attributes which a substance has at different times are all pre- 
dicates of the substance, and though any attribute exists only 
at a certain time, yet the fact of its being an attribute at that ' 
time is eternally a predicate of the substance in question. For 
the substance is the same subject at all times, and therefore 
has always the same predicates, since the notion of the predi- ' 
cate, according to Leibniz, is always contained in the notion of 
the subject. All my states and their connections have always 
been in the notion of that subject which is /. Thus to say 
that all my states are involved in the notion of me, is merely to 
say that the predicate is in the subject (G. ii. 43). From this ! 
-proposition, Leibniz continues, it follows that every soul is a ' 
world apart, independent of everything else except God (G. ii. 
46, 47). For since all my predicates have always belonged to 
me, and since among these predicates are contained all my 
states at the various moments of time, it follows that my i 
development in time is a mere consequence of my notion, and' 
cannot depend upon any other substance. Such a subject as I 

' In his youth, Leibniz was inclined to admit space as a substance. See 
G. I. 10 (1668), and Selver, op. cit. p. 28. 



44 THE CONCEPTION OF SUBSTANCE. 

am may not exist; but if such a subject does exist, all my 
states follow from the fact that I am such as I am, and this 
suffices to account for my changes, without supposing that I 
am acted upon from without ^ 

18. We can now understand what Leibniz means by 
activity. The activity of substances, he says, is metaphysically 
necessary (G. ii. 169). It is in this_ activity that tlie_ very 
substance of things consists. Without a force of some dura- 
tion, no created substance would remain numerically the same, 
but all things would be only modifications of one divine sub- 
stance (D. 117 ; G. IV. 508)1 Substance, again, is a_b§iiig 
capable_of_action (D. 209 ; L. 406 ; G. VI. 598). But he does 
not often explain clearly what he means by activity. (^Activity 
is, as a rule, a cover for confused thinking ;) it is one of those 
notions which, by appealing to psychological imagination, 
appear to make things clear, when in reality they merely give 

I an analogy to something familiar. Leibniz's use of activity, 

1 however, does not seem open to this charge. He definitely 
rejects the appeal to imagination. The indwelling force of 
substances, he says, may be conceived distinctly, but not 
explained by images, for force must be grasped by the under- 

' standing, not the imagination (D. 116 ; G. IV. 507). What 
then is this activity, which can be clearly conceived, but not 

1 imagined? 

Without an internal force of action, Leibniz explains, a 

I thing could not be a substance, for the nature of substance 
consists in this regulated tendgncy, from which phenomena are 

: born in order (G. III. 58). Again he says (L. 300, n. ; G. IV. 

1 Arnauld's judgment upon this theory, immediately after reading the 
Diacours de Mitaphysique, deserves quotation as a warning to philosophers 
who feel tempted to condemn their juniors. "I have at present," he writes, 
"such a cold, that all I can do is teU your Highness, in two words, that I 
find in these thoughts so many things which alarm me, and which almost all 
men, if I am not mistaken, will find so shocking, that I do not see of what use 
a writing can be, which apparently all the world will reject. I shall only give 
as an instance what he says in Art. 13: 'That the individual notion of each 
person involves once for all everything that will ever happen to him ' " (G. ii. 15). 

I The selection of this remark as specially shocking may perhaps help to account 

I for Leibniz's omission of it from his published works. 

^ Cf. Spinoza, Ethics, m. 6, 7. For him also, individuality consists in 
activity. Cf. Pollock's Spinoza, 1st ed. pp. 217, 221 ; 2nd ed. pp. 201, 205. 



THE CONCEPTION OF SUBSTANCE. 45 

472) : " By force or power {puissance), I do not mean the | 
capacity (pouvoir) or mere faculty, which is nothing but a ■ 
near possibility of acting, and which, being as it were dead, 
never produces an action without being stimulated from with- 
out, but I mean something between the capacity {pouvoir) and 
action, something which includes an effort, an act, an entelechy, 
for force passes of itself into action, in so far as nothing hinders 
it. Wherefore I regard force as constitu tive of substance, since f 
it is the principle of action, which is the characteristic of 
substance." We can thus see what Leibniz means by activity, 
and we can see also that this notion is a necessary and legiti- 
mate consequence of his notion of substance. A substance, we 
have seen, is a subject which has predicates consisting of various 
attributes at various parts of time. We have seen also that all 
these predicates are involved in the notion of the subject, and 
that the ground of its varying attributes is, therefore, within 
the substance, and not to be sought in the influence of the 
outside world. Hence there must be, in every state of a. \ r 
substance, some element or quality in virtue of which that ! 
state is not permanent, but tends to pass into the next state. 
This element is what Leibniz means by activity'. (^Activity is , 
to be distinguished from what we mean by causation. Causa- 
tion is a relation between two phenomena in virtue of which 
one is succeeded by the other. Activity is a quality of one 
phenomenon in virtue of which it tends to^cause another. 
Activity is an attribute corresponding to the relation of causality ; | 
it is an attribute which must belong to the subject of changing 
states, in so far as those states are developed out of the nature 
of the subject itself Activity is not a mere relation ; it is an i 
actual quality of a substance, forming an element in each state I 
of the substance, in virtue of which that state is not permanent, 
but tends to give place to another.) Since a substance, as we [ 
have seen, is essentially the permanent subject of changing 
attributes, it follows that activity, in the above sense, is essen- 
tial to substance, and thus metaphysically necessary. It follows 
also that, as Leibniz says, without activity a substance could 
not preserve its numerical identity ; for without activity a sub- 
stance would cease to have new attributes at new moments of 
1 Of. D. 115; G. IV. 506— 7. 



46 THE CONCEPTION OF SUBSTANCE. 

time, and would thus cease to exist. Activity thus follows 
from the general doctrine, which Leibniz shares with many 
other philosophers {e.g. Lotze), that every relation must be 
analyzable into adjectives of the related terms. Two states 
have a relation of succession and causality ; therefore there 
must be corresponding adjectives of the states. The adjective 
of the preceding state is activity. Passivity, however, is not 
the adjective of the succeeding state, but is something quite 
different \ 

I 19. We may now retijjn to the law of sufEcignt reason, 
i I and interpret it in connection with activity. Although, as we 
' , saw, all the states of a substance are contained in its notion, 
and could, by perfect knowledge, be deduced from its notion, 
/ yet this, as Leibniz means it, amounts to little more than the 
1 law of identity ==. Whatever my future actions may be, it must 
be true now that they will be such as they will be. Whoever 
[ acted otherwise would not be the same person. But that I 
' shall act in any specific manner cannot be inferred from any 
! general proposition about me. My specific actions are con- 
nected with the notion of me, but are not related necessarily to 
I any of my general qualities or to each other. There is nothing 
in me, Leibniz says, of all that can be conceived generally, or 
by essence, or by a specific or incomplete notion, from which 
my future actions follow necessarily. Nevertheless, if I am 
going to take a journey, it is certain that I shall take it, and 
therefore, if I did not take it, there would be falsity, which 
would destroy the individual or complete notion of me (G. II. 
52). That is to say, whoever did otherwise would not be the 
same person. CThis really amounts to no more than (1) the 
assertion of permanent substances, (2) the obvious fact that 
every proposition about the future is already determined either 
as true or as false, though we may be unable to decide the 
\ alternative.^Thus we have no means, in all this, of determining, 
! from a given state of substance, what its future states will be ; 
and for this purpose, according to Leibniz, we require the prin- 
I ciple of sufficient reason. 
^ ! The principle fulfils, therefore, the same function as that 

1 Cf. Chap. XII, § 84. 

2 Of. G. II. 42, beginning ot paragraph. 



THE CONCEPTION OF SUBSTANCE. 47 

for which causality is now used ; it gives a connection between i 

events at dififerent times. But unlike causality, it endeavours 1 

to show why, and not merely that, certain sequences occur. In \ 

an early letter, written before Leibniz had discovered his notion 

of substance (1676 ?), he urges that a single thing cannot be 

the cause of its changes, since everything remains in the state 

it is in, if there is nothing to change it ; for no reason can be 

given in favour of one change rather than another (G. i. 372). 

By the contrast between this and his later opinions, we see 

clearly the connection between activity and sufficient reason. 

The sufficient reason for one change rather than another is to 

be found in the nature of activity. In substances which are . 

not free, this activity is regulated by general laws, which them- | y^ « 

selves have a sufficient reason in God's perception of fitness ; in , 

free substances, the sufficient reason lies in the more or less J 

confused perception of the good on the part of the substance 

itself. But in no case is the connection between two states in 

itself necessary ; it always arises from the perception, either in 

God or in the creature (if this be free), that the change is good 

(G. II. 38). This topic, however, cannot be fully discussed 

until we have examined the doctrine of Monads. 

20. From what has been said of activity, it is plain that 
those predicates of a given substance which are existents in 
time form one causal series. Leibniz sometimes goes so far in i 
this direction as to approach very near to Lotze's doctrine that « 
things are laws^ (All singular things, he says, are subject to i 
succession, nor is there anything permanent but the law itself, 
involving continual succession.^ Successions, he continues, like 
such series as numbers, have the property that, given the first 
term and the law of progression, the remaining terms arise in 
order. The only difference is, that in successions the order is 
temporal, but in numbers the order is that of logical priority 
(G. II. 263). Further, the persistence of the same law is the 
ground for asserting that a new temporal existent belongs to 
the same substance as a past existent. The identity of a sub- 
stance at different times is recognized, he says, " by the persist- 
ence of the same law of the series, or of continuous simple 
transition, which leads us to the opinion that one and the 
1 See Lotze's Metaphysic, Book I. Chap. III., especially § 32. 



48 THE CONCEPTION OF SUBSTANCE. 

same subject or monad is changing. That there should be a 
persistent law, involving the future states of that which we 
conceive as the same, is just what I assert to constitute it the 
same substance" (G. ii. 264). These passages explain very 
definitely what Leibniz means by his phrase, that each monad 
contains in its nature the law of the continuation of the series 

i'of its operations (D. 38; G. II. 13G). They enable us, also, to 
see what would remain of the doctrine of monads if the appeal 

, to substance were dropped. (All the predicates of a given 
substance form one causal series : this series might, therefore, be 
taken as defining what we are to mean by one substance, and 
the reference to subject and predicate might be dropped.") The 
plurality of substances would then consist in the doctrine, that 
a given existent at a given moment is caused, not by the whole 
preceding state of the universe, but by some one definite existent 
in the preceding moment. This assumption is involved in the 

• ordinary search for causes of particulars. It is supposed, for 
instance, that two simultaneous existents A and B have been 
caused, respectively, by two different preceding existents a and 
/8, not that each was caused by the whole preceding state of 
the universe. This assumption, if justified, would be sufficient 
to establish something very like Leibniz's philosophy. For A 
and B will in turn cause, respectively, different existents A' and 

' B', and so on. The denial of the interaction of substances thus 
reduces itself, when the series is substituted for the single 
subject, to the assertion that there are many causal series, and 
not one only. ( I shall return to this assertion when I come to 

I Leibniz's grounds for a plurality of substances \) At present I 
wish to point out how easily Leibniz could have got rid, at this 
stage, of the appeal to subject and predicate, and have sub- 

I stituted the unity of the law or series for that of the logical 
subject — a doctrine from which, as from his own, the persist- 

! ence and independence of substances necessarily follows. 

21. (^At this point it may be well to enquire how, in 
Leibniz's view, a substapce differs from the sum of its prgdi- 

! cates.^ If the monad had been reduced to a mere causal series, 

it would have been identified with the sum of its predicates. 

It would then have had a purely formal unity ; there would not 

' See end of Chap. VII. 



THE CONCEPTION OF SUBSTANCE. 49 

have been an actual subject, the same at all points of time, but 
only a series of perpetually new terms. There would still have | 
been simple substances, in the sense of in dependent causal 
series, but there would have been no reason for regarding the 
soul as one of these simple substances, or for denying causal 
interaction between my states and other existents. On the 
contrary, it is because the Ego appeared to Leibniz to be 
evidently one subject, that its various states were held to 
constitute one independent causal series. We must not say, raj- 
therefore, as is often loosely done, that Leibniz identified sub- ' j^, i v' 
stance and activity ; activity is the essence of substances, but ' 
substances themselves are not essences, but the subjects of , 
essences and other predicates^ Thus a substance is not, for i 
Leibniz, identical with the sum of its states '■' ; on the contrary, 
those states cannot exist without a substance in which to 
inhere. The ground for assuming substances — and this is a I « 
very important point — is purely and solely logical. What i 
Science deals with are states of substances, and it is these only 
that can be given in experience. They are assumed to be 
states of substances, because they are held to be of the logical 
nature of predicates, and thus to demand subjects of which they 
may be predicated. The whole doctrine depends, throughout, i 
upon this purely logical tenet. (^And this brings us back to the 1 
distinction, which we made in Chapter II., between two kinds 
of subject-predicate proposition. The kind which is appro- 
priate to contingent truths, to predications concerning actual 
substances, is the kind which says " This is a man," not " man 
is rational.") Here this must be supposed defined, not primarily i 
by predicates, but simply as that substance which it is. The 1 

1 Cf. D. 118; G. IV. 509: "As for me, as far as I believe myself to have 
grasped the notion of action, I hold that that most received philosophical dogma, 
that actions belong to subjects {esse suppositorum), follows from it, and is proved 
by it ; and I think that this principle is so true that it is also reciprocal, so 
that not only whatever acts is a single substance, but also that every single 
substance acts without iutermission." It appears plainly, from this passage, 
that the substance is conceived as a permanent subject, so that the assertion of 
activity is significant, and not a mere tautology. '^ -i-W . S.'- . y -»/r , 

2 Cf. G. II. 263: "Substances are not wholes which contain parts /ormaMtcr, 
but complete things which contain partial ones eminenter." Cf. also G. vi. 
350. 

B. 1. 4 



50 THE CONCEPTION OF SUBSTANCE. 

substance is not an idea, or a predicate, or a collection of predi- 
cates; it is the substratum in which predicates inhere (cf. N. E. 
pp. 225 — 6 ; G. v. 201 — 3 ; esp. § 2). It would seem, however, 
that the word this must mean something, and that only a 
meaning is capable of distinguishing which substance we are 
speaking of What is usually meant is some reference to time 
or place, so that " this is human " would reduce itself to " hu- 
manity exists here." The reference to time and place is to 
some extent countenanced by Leibniz (see e.g. G.' Ii. 49), but 
he regarded time and place as themselves ultimately reducible 

j to predicates. Thus the substance remains, apart from its 

I predicates, wholly destitute of meaning'. (As to the way in 
which a term wholly destitute of meaning can be logically 
employed, or can be valuable in Metaphysics, I confess that I 

I share Locke's wonder^) When we come to the Identity of 
Indiscernibles, we shall find that Leibniz himself, by holding a 
substance to be defined by its predicates, fell into the error of 
confounding it with the sum of those predicates. (That this 
was from his stand-point an error, is sufficiently evident, since 
there would be no ground for opposing subjects to predicates, 
if subjects were nothing but collections of predicates.) More- 
over, if this were the case, predications concerning actual 
substances would be just as analytic as those concerning 
essences or species, while the judgment that a substance 
exists would not be one judgment, but as many judgments 

' as the subject has temporal predicates. Confusion on this point 
seems, in fact, to be largely responsible for the whole theory of 
analytic judgments. 

22. The relation of time to Leibniz's notion of substance is 

I difficult clearly to understand. (Is the reality of time assumed 
as a premiss, and denied as a conclusion ? ) A substance, we 

' have seen, is essentially a subject persisting in time. But by 
the doctrine that all the states of a substance are eternally its 
predicates, Leibniz endeavours to eliminate the dependence 

' Mr Bradley, in attempting to reduce all judgment to predication about 
Eeality, is led to the same view concerning his ultimate subject. Eeality, for 
him, is not an idea, and is therefore, one must suppose, meaningless. See his 
Logic, pp. 43, 49, 50, 66. 

2 Essay, Book II, Chap. XXIII. §| 1, 2; N, B. pp. 225—6. 



THE CONCEPTION OF SUBSTANCE. 51 

upon time. There is, however, no possible way, so far as I can 
discover, in which such an elimination can be ultimately 
effected. For we must distinguish between the state of the 
substance at a given moment, and the fact that such is its state 
at the given moment. The latter only is eternal, and there- ' 
fore the latter only is what Leibniz must take as the pre- 
dicate of the substance. The present state exists now, and 
does not exist the next moment ; it cannot itself, therefore, 
be eternally a predicate of its substance. The eternal pre- : 
dicate is that the substance has such and such a state at 
such and such a moment. The pretended predicate, therefore, 
resolves itself into a proposition, which proposition itself is 
not one of subject and predicate. This point is well illus- 
trated by a passage in which Leibniz endeavours to explain 
how an eternal predicate may refer to one part of time. What 
follows from the nature of a thing, he says, may follow per- 
petually or for a time. When a body moves in a straight line 
under no forces, it follows that at a given moment it will be at 
a given point, but not that it will stay there for ever (G. Ii. 
258). What follows, in this case, for a time, is itself a proposi- 
tion, and one logically prior to the attempted subsequent predi- 
cation. This instance should make it plain that such proposi- 
tions cannot be validly reduced to predications. 

The doctrine of activity, however, seems designed to free such ' 
propositions from all reference to actual parts of time, and thus 
to render the propositions concerning states of a substance 
at different times merely complex predicates, (it is necessary 
for Leibniz to maintain that to exist now and to exist then do not 
differ intrinsically, but only differ in virtue of some relation 
between what exists now and what existed then ; and further, 
that this relation is due to the quality of what exists in these 
different times.) This is attempted by the notion of activity. 
In order to avoid the relation to moments of time, these 
moments must be reduced to elements or parts of the corre- 
sponding states. Now activity is supposed to make a difference 
of quality between preceding and succeeding states, by means 
of which we could interpret their order of succession as a result 
of their own natures. The preceding state is the desire, the 
succeeding state the desired — such is, roughly speaking, the 

4—2 



^r '^•-~ 



52 THE CONCEPTION OF SUBSTANCE. 

J difference of states, to which it is sought to reduce the temporal 
I difference. But this attempt, I think, cannot be successful. 
In the first place, few people would be willing to admit, what 
follows from the doctrine, that it is a pure tautology to say that 
^l activity or desire is directed to the future. In the second 
j place, the present doctrine cannot explain what is meant by 
1 the simultaneity of states of different substances. If simul- 
taneity be admitted, it follows that the present or any other 
time is not merely in my mind, but is something single and 
' unique in respect of which simultaneous states agree. There 
/ , is, in short, one time, not as many times as there are substances. 
Hence the time-order cannot be merely something in my mind, 
I or a set of relations holding between my states. In the third 
place, it may be questioned what we gain by substituting the 
I order due to activity for that due to time. We have a series 
of states A, B, C, D,..., such that A's activity refers to B, B's 
refers to C, and so on. We then say that the order thus 
obtained is what the time-order really means. The difficulty 
is, to understand the relation of the activity of A to the B 
which it refers to. (It seems essential that the object of activity 
or desire should be non-existent, but should be regarded as 
f ! capable of becoming existent.) In this way, reference to future 
' time seems to be a part of the meaning of activity, and the 
attempt_to infer time Jiwu activity thus involves a vicious 
1 circle . Then again, the definition of one state of a substance 
seems impossible without time. A state is not simple ; on the 
contrary, it is infinitely complex. It contains traces of all past 
states, and is big with all future states. It is further a reflec- 
( tion of all simultaneous states of other substances. Thus no 
I way remains of defining one state, except as the state at one 
i time. And finally, all states consist of perceptions, and desires 
for perceptions, either of the world or of the eternal truths. 
Now the perceptions involved in mirroring the universe — from 
which all knowledge of actual existence is derived — presuppose 
simultaneity in their definition. This point will be proved 
when we come to deal with perception, and the general doctrine 
I of time will be dealt with again in connection with space. I 
j shall then endeavour to show, that there must be one and the 
I same order among the states of all substances, and that this 



THE CONCEPTION OF SUBSTANCE. 53 

order, consequently, cannot depend upon the states of any one i 
substance. i 

Thus time is necessarily presupposed in Leibniz's treatment i f 
of substance. That it is denied in the conclusion, is not a 
triumph, but a contradiction. (^A precisely similar result will 
appear as regards space, when we come to the grounds for the 
plurality of substances.) We shall find that Leibniz made 
a constant endeavour to eliminate, by s\ibsequent fruitless 
criticism, these indispensable, but, for him, inadmissible 
premisses. 



54 



CHAPTEK V. 



THE IDENTITY OF INDISCERNIBLES AND THE LAW OF 
CONTINUITY. 

POSSIBILITY AND COMPOSSIBILITY. 

23. I COME now to the last of Leibniz's general logical 
principles. The Identity of Indiscernibles and the Law of 
Continuity are closely connected, though not deducible one 
from the other. They are both included in the statement 
that all created substances form a series, in which every 
possible position intermediate between the first and last terms 
is filled once and only once. That every possible position is 
filled once is the Law of Continuity; that it is filled only 
once is added by the Identity of Indiscernibles. I shall discuss 
the latter principle first. We shall have to enquire (1) what 
it means, (2) how Leibniz established it, (3) how far his 
arguments in support of it were valid. 

(1) There is no difficulty as to the meaning of the Identity 
of Indiscernibles. It is not, like the principle of sufficient 
reason, stated in different ways at different times. It asserts 
"that there are not in nature two indiscernible real absolute 
beings " (D. 259 ; G. vii. 393), or again that " no two sub- 
stances are completely similar, or differ solo numero" (G. IV. 
433). It applies to substances only ; existent attributes, as 
Leibniz explains in discussing place (D. 266 ; G. vii. 400, 401), 
may be indiscernible. Leibniz's doctrine is not that urged by 
Mr Bi-adley, that all diversity must be diversity of content. If 
this were the principle, it would be far more fundamental, and 



THE IDENTITY OF INDISCERNIBLES. 55 

would have to be considered before the definition of substance. 
The principle, so far from maintaining diversity of content 
alone, presupposes material or numerical diversity as well as 
diversity of content proper. To both these it is logically 
subsequent. Diversity of content proper is the difference 
between one content and another. Material or numerical 
diversity is the difference between one subject, or one sub- 
stance, and another. Leibniz's doctrine is, that two things 
which are materially diverse, i.e. two different substances, 
always differ also as to their predicates. This doctrine evi- 
dently presupposes both kinds of diversity, and asserts a relation 
between them. Diversity of content is sometimes also used in 
this latter sense, as meaning that difference, between two 
subjects, which consists in their having different predicates. 
But as this sense is complex, and composed of the two other 
kinds of diversity, it is better to restrict the term diversity of 
content to the former sense, i.e. the difference between contents. 
The doctrine is, therefore, that any two substances differ as to 
their predicates. It thus presupposes a knowledge of substance, 
and could not be discussed until substance had been defined. 

24. (2) This principle is not, like the Law of Sufficient 
Reason, a premiss of Leibniz's philosophy. It is deduced and 
proved in many passages. But the proofs are various, not only 
in their methods but even in their results. For once at least the 
principle appears as merely contingent, like the laws of motion, 
at other times as metaphysically necessary. In such cases of 
inconsistency, it is well to decide, if possible, which alternative 
suits the rest of the system best, and which, if the inconsistency 
had been pointed out, the philosopher would have chosen. I 
holdjhatjjeibniz should have regarded his principle as neces- 
sary. For the proof of this, we will examine his various 
grounds. 

In the fifth letter to Clarke, Leibniz says : " This supposition 

of two indiscernibles seems indeed to be possible in abstract 

terms ; but it is not consistent with the order of things, nor 
with the divine wisdom, by which nothing is admitted without 
reason '' (D. 259 ; G. vii. 394). He continues : " When I deny 
that there are two drops of water perfectly alike, or any two 
other bodies perfectly indiscernible from each other; I don't 



56 THE IDENTITY OF INDISCERNIBLES. 

say, 'tis absolutely impossible to suppose (poser) them; but 
that 'tis a thing contrary to the divine wisdom, and which 
consequently does not exist. I own that if two things per- 
fectly indiscernible from each other did exist, they would be 
two; but that supposition is false, and contrary to the grand 
principle of reason" (D. 260; G. VII. 394—5). In the pre- 
ceding paper (D. 247 ; G. vii. 371 — 2) he deduces the Identity 
of Indiscernibles from the Law of Sufficient Reason, saying that 
God could have no reason for placing one of two indiscernibles 
here, the other there, rather than for adopting the opposite 
arrangement; This argument, however, though it is, of all his 
arguments for the principle, the least d priori and the least 
cogent, yet gives metaphysical necessity, for we saw, in 
Chapter III., that the need for some sufficient reason is meta- 
physically necessary (G. ii. 420). Thus negative conclusions 
from this principle^i.e. such a proposition is false, because it 
could have no sufficient reason — are necessary, though positive 
conclusions, where a specific sufficient reason is assigned, may be 
contingent. Accordingly, he concludes the above proof with the 
remark that to suppose two things indiscernible is to suppose 
the same thing under different names (D. 247 ; G. Vli. 372). 
f The passage asserting indiscernibles to be possible — which, so 
far as I know, is the only one — was probably due, therefore, to 
the fact that he was deducing their non-existence from the 
principle of Sufficient Reason, and that this principle generally 
gives contingent results. And it is difficult to be sure how 
great a reservation is implied by the words "in abstract 
terms." 

The above argument for his principle is far from cogent as 
it stands, and does not adequately represent his meaning. It 
seems to presuppose here and there as sources of numerical 
diversity, and then to infer that there must be some further 
and apparently unconnected difference besides that of position. 
What he really means, however, is that here and there must 
themselves be reduced to predicates, in accordance with his 
general logic. This is attempted by his theory of space, which 
will be examined later. What I want to insist on, however, is, 
that the differentiation must not be supposed effected by differ- 
ence of place, per se, but by difference as to the predicates to 



THE IDENTITY OF INDISCERNIBLES. 57 

which, on Leibniz's theory, place must be reduced. Where 
difference of place appears, there must be difference of predicates, 
the latter being the truth of which the former is a confused 
expression. Thus to assert that two substances cannot be in 
the same place at the same time, is to assert a proposition 
logically subsequent to the Identity of Indiscernibles. The 
proof which starts from difference of place is, therefore, merely 
ad hominem, and does not represent the gist of the principle. 
Clarke is willing to admit that two things must differ in place ; 
hence, since place is a predicate, they must have different 
predicates. Thus Leibniz says (N. E. 238; G. V. 213) that 
besides the difference of time and place there must be an 
internal principle of distinction, and adds that places and times 
are distinguished by means of things, not vice versa. Again he 
says (G. II. 250) that things which differ in place must express 
their place, and thus differ not only in place or in an extrinsic 
denomination. He no doubt reliedT^ a rule, on his readers 
admitting that two things could not co-exist in one spatio-tem- 
poral point, and would thus deduce an intrinsic difference from 
this admission. But with his theory of space and time, he 
could not logically rely upon this argument, as he used the 
Identity of Indiscernibles to disprove the reality of space and 
time. He had also another and more abstract ground, derived 
from the nature of substance, and closely connected with the 
logical doctrines which we have already examined. If he had 
not had such a ground, he would have been involved in many 
hopeless difficulties. For he declares (D. 273 ; G. vii. 407) 
that God will never choose among indiscernibles, which is, 
indeed, a direct result of sufficient reason. Consequently we 
must infer that, among all actual substances, there is none to. 
which another precisely similar substance can be even con- 
ceived. For if it were possible to conceive another, God would 
have conceived it, and therefore could not have created either. 
The proof that, where the notions concerned are notions of 
substances, indiscernibles are inconceivable, is to be found in 
Leibniz, and must now be examiined. 

The nature of an individual substance or complete being, 
Leibniz says, is to have so complete a notion that it suffices for 
comprehending and deducing all the predicates of the subject 




58 THE IDENTITY OF INDISCERNIBLES. 

of the notion'. "From this," he continues, "follow several 
considerable paradoxes, as, among others, that it is not true 
that two substances resemble each other completely, and differ 
only numerically" (G. iv. 433). In this argument, several 
intermediate steps seem to have been omitted, I suppose 
because Leibniz thought tbem obvious. I cannot find these 
steps anywhere explicitly stated, but I imagine his argument 
might be put as follows. All that can be validly said about a 
substance consists in assigning its predicates. Every extrinsic 
denomination — i.e. every relation — has an intrinsic foundation, 
i.e. a corresponding predicate (G. ii. 240). The substance is, 
therefore, wholly defined when all its predicates are enumerated, 
so that no way remains in which the substance could fail to be 
unique. For suppose A and B were two indiscernible sub- 
stances. Then A would differ from B exactly as B would differ 
from A. They would, as Leibniz once remarks regarding 
atoms, be different though without a difference (N. E. p. 309 ; 
G. V. 268). Or we may put the argument thus : A differs from 
B, in the sense that they are different substances ; but to 
be thus different is to have a relation to B. This relation must 
have a corresponding predicate of A. But since B does not 
differ from itself, B cannot have the same predicate. Hence A 
and B will differ as to predicates, contrary to the hypothesis. 
Indeed, if we admit that nothing can be said about a substance 
except to assign its predicates, it seems evident that to be a 
different substance is to have different predicates. For if not, 
there would be something other than predicates involved in 
determining a substance, since, when these were all assigned, 
the substance would still be undetermined. 

25. (3) This argument is valid, I think, to the extent of 
pXQxing that, if subject and predicate be the canonical form of 
propositions, there cannot be two indiscernible substances. The 
difficulty is, to prevent its proving that there cannot be two 
ubstances at all. For the numerical diversity of the substances 

1 See Appendix, § 17. So Wolff says {Logic, Chap. I. § 27): "All that we 
conceive, or all that is found, in an individual, is determined in every respect ; 
and it is by this very fact, that a thing is determined, both as to what consti- 
tutes its essence, and as to what is accidental to it, that it acquires the quality 
ot individual." 



THE IDENTITY OF INDISCEENIBLES. 59 

is logically prior to their diversity as to predicates : there can 
be no question of their differing in respect of predicates, unless 
they first differ numerically. But the bare judgment of nu- 
merical diversity itself is open to all the objections which 
Leibniz can urge against indiscernibles '. Until predicates 
have been assigned, the two substances remaiji indiscernible ; 
but they cannot have predicates by which they cease to be 
indiscernible, unless they are first distinguished as numerically 
different. Thus on the principles of Leibniz's logic, the Identity 
of Indiscernibles does not go far enough. He should, like 
Spinoza, have admitted only one substance. On any other 
logic, there can be no ground against the existence of the same 
collection of qualities in different places, since the adverse 
proof rests wholly on the denial of relations. But as a different 
logic destroys substance, it destroys also anything resembling 
Leibniz's statement of his principle. 

But further, the argument seems to show an objection — the 
same which was suggested in the last Chapter — against the 
whole doctrine of substance. If a substance is only defined by 
its predicates — and this is essential to the Identity of In- 
discernibles — then it would seem to be identical with the sum 
of those predicates. In that case, to say that such and such a 
substance exists, is merely a compendious way- of saying that 
all its predicates exist. Predicates do not inhere in the sub- 
stance in any other sense than that in which letters inhere in 
the alphabet. The logically prior judgments are those asserting 
the existence of the various predicates, and the substance is no 
longer something distinct from them, which they determine, 
but is merely all those predicates taken together. But this, as 
we have already seen, is not what Leibniz intends to say. The 
substance is a single simple indivisible thing, persisting through 
time ; it is not the same as the series of its states, but is the 
subjeet of them. But in this case, a substance is not properly 
speaking defined by its predicates. There is a difference between 
asserting a given predicate of one substance, and asserting it of 
another. The substance can only be defined as "this." Or 
rather — and this is where the doctrine of substance breaks 
down — the substance cannot be defined at all. To define is 
1 Cf. the proof of Prop. V. Book I. of Spinoza's Ethics. 



60 THE IDENTITY OF INDISCEENIBLES. 

to point out the meaning, but a substance is, by its very 
nature, destitute of meaning, since it is only the predicates 
which give a meaning to it. Even to say "this," is to indi- 
cate some part of space or time, or some distinctive quality; 
to explain in any way which substance we mean, is to give 
our substance some predicate. But unless we already know 
which substance we are speaking of, our judgment has no 
definiteness, since it is a different judgment to assert the same 
predicate of another substance. Thus we necessarily incur a 
vicious circle. The substance must be numerically determi- 
nate before predication, but only predicates give numerical 
determination. Either a substance is wholly meaningless, and 
in that case cannot be distinguished from any other: or a 
substance is merely all or some of the qualities which are 
supposed to be its predicates. These difficulties are the in- 
variable result of admitting, as elements of propositions, any 
terms which are destitute of meaning, i.e. any terms which 
are not what may be called ideas or concepts. As against many 
substances, we may urge, with Mr Bradley, that all diversity 
must be diversity of meanings ; as against one substance, we may 
urge that the same is true of identity. And this holds equally 
against the supposed self-identity of Mr Bradley's Reality. 

26. Connected with the Identity of Indiscernibles is the 
assertion that every substance has an infinite number of pre- 
dicates. That this must be the case, is evident from the mere 
fact that every substance must have a predicate corresponding 
to every moment of time. But Leibniz goes further than this. 
The state of a substance at each moment is analyzable into an 
infinite number of predicates. This might itself be deduced 
from the fact that the present state has relations to all past 
and future states, which relations, according to Leibniz, must 
affect the present state — indeed it is in this that their truth 
consists. But another factor is the representation of the whole 
universe, which necessarily involves infinite complexity in each 
state of each substance. This infinite complexity is a mark of 
the contingent. There is a difference, Leibniz says, between 
the analysis of the necessary and that of the contingent. The 
analysis from the subsequent by nature to the prior by nature 
comes to an end in necessary matter with the primitive notions. 



THE IDENTITY OP INDISGERNIBLES. 



61 



as the analysis of numbers ends with unity. But in contingents 
or existents, this analysis goes to infinity, without ever reaching 
primitive elements (G. III. 582). Again he points out that it is 
impossible for us to have knowledge of individuals, and to 
determine exactly the individuality of anything. For individu- 
ality includes infinity, and only one who understands infinity 
can know the principle of individuation of this or that thing 
(N. E. 309; G. v. 268). Necessary and contingent truths 
differ as rational numbers and surds. The resolution of the 
latter proceeds to infinity (G. vii. 309). 

Again he says (G. vii. 200) : " The difference between 
necessary and contingent truths is indeed the same as that 
between commensurable and incommensurable numbers. For 
the reduction of commensurable numbers to a common mea- 
sure is analogous to the demonstration of necessary truths, or 
their reduction to such as are identical. But as, in the case of 
surd ratios, the reduction involves an infinite process, and yet 
approaches a common measure, so that a definite but unending 
series is obtained, so also contingent truths require an infinite 
analysis, which God alone can accomplish." 

I am afraid Leibniz regarded this, to some extent, as a 
confirmation of his doctrine of contingency. He seems to have 
thought it natural that the contingent should be that which we 
cannot perfectly understand ; he says, for example, that God 
alone sees how I and existence are joined, and knows d priori 
the cause of Alexander's death'. The world of contingents is 
characterized, not only by the fact that it exists, but also by the 
fact that everything in it involves infinity by its infinite com- 
plexity, and is thus inaccessible to exact human knowledge. 

Such passages have led many commentators to think that 
the difference between the necessary and the contingent has an 
essential reference to our human limitations, and does not 
subsist for God. This view, I think, rests upon a confusion, 
and does quite undue damage to Leibniz's system. The confu- 
sion is between the general character of all contingents, actual 
as well as possible — for possible worlds involve the same infinite 
complexity, which indeed is a necessary result of time —and the 
meaning of contingency itself. It is metaphysically necessary 
1 G. IV. 433; v. 392 (N. E. 469). 



.v^' 



^*' 



62 THE IDENTITY OF INDISCERNIBLES. 

that the contingent should be thus complex ; but what makes 
contingency is not complexity, but existence. Or, to put the 
matter otherwise, the confusion is between eternal truths about 
the contingent — i.e. the necessary propositions about the natures 
of substances — and the contingent truth that such substances 
exist. This distinction must be made — though Leibniz may 
have been guilty of some confusion in the matter — for many 
' very weighty reasons. In the first place, truths about possible 
! worlds c anno t be_contingent, and all truths about the actual 
world are, when robbed of the assertion of actual existence, 
I truths about one among possible worlds. In the second place, 
I God was free, in creation, because of the other possible worlds : 
1 his choice was contingent. And his freedom, as well as that of 
creatures, can only result if contingency is metaphysically true, 
and no mere delusion. In the third place, the Law of Sufficient 
Reason, in the sense in which it asserts final causes, is coordi- 
nate with the Law of Contradiction, and applies to God's acts 
just as much as to the actual world ; whereas, on the opposite 
view, Leibniz's belief that he used two principles has to be 
I declared erroneous. The doctrines of final causes, of possible 
worlds, of the synthetic nature of causal connections, and of 
'• freedom — everything, in fact, that is characteristic of Leibniz — 
1 depends upon the ultimately irreducible nature of the opposi- 
I tion between existential and necessary propositions. Thus we 
must maintain that Leibniz does not only mean, by contingent, 
that which we cannot fully explain. But he cannot be absolved, 
I fear, from dwelling with pleasure on this supposed confirma- 
tion of the twofold nature of propositions. 
f Here again, I think, as throughout, Leibniz is not clear as 
: to the difference between the relation of individual to species, 
and that of species to genus. He sometimes urges that there is 
no difference between these two relations — a view to which I 
see no objection, except that it is inconsistent with his notion 
of individual substance. This view underlies, as we saw, the 
Identity of Indiscernibles, and is suggested in the New Essays, 
where, however, it leads to results which he ought to have found 
very inconvenient. " In mathematical strictness," he says, "the 
least difference making two things in any respect dissimilar, 
makes them different in species In this sense, two 



THE LAW OF CONTINUITY. 63 

physical individuals will never be perfectly similar, and what is 
more, the same individual will pass from species to species, for 
it is never wholly similar to itself even for more than a moment'" 
(N. E. 335—6 ; G. v. 287—8). His view seems to be that, in 
eternal truths, we start with essences and predicates, and 
determine their relations ; while in contingent truths, we start 
with the existence of something undetermined, such as the Ego, 
and enquire into its predicates. The question is, in this case, 
what is the nature of this existent ? And since every substance 
has an infinite number of predicates, the question is one which 
we can never fully answer. But it is evident — -though Leibniz 
would seem not to have perceived it — that in starting with the 
Ego, or any other existent, we must already have determined some 
unique property of our substance, or else we should not know 
which we were speaking of, and the question would be wholly 
indeterminate. Spatio-temporal position is, I think, always 
covertly assumed in such questions, and it is this assumption 
alone which gives them a definite meaning and a definite answer. 

27. The infinite complexity of substances will help us in 
dealing with our next topic, the Law of Continuity. This law 
usually holds a prominent place in expositions of Leibniz, but I 
cannot discover that, except as applied to Mathematics, it has 
any great importance. (There are three distinct kinds of con- 
tinuity, all of which Leibniz asserts. None of them, he thinks, 
has metaphysical necessity, but all are regarded as required by 
the '"order of things.") These three kinds are (1) spatio-tem- 
poral continuity, (2) what may be called continuity of cases, 
(3) the continuity of actual existents or of forms. Let us 
consider these in turn. 

(1) Spatio-temporal continuity is itself twofold. There is 
the continuity of space and time themselves, which Leibniz 
admits to be metaphysically necessary; and there is the con- 
tinuity of what exists in space and time. The former is not 
in question here. The latter includes motion and aJJ ot^er ki^ds j 
of chgjige. As regards change, it is generally admitted that 

^ It seems probable that Leibniz does not mean, by a "physical individual," 
a single substance, for if he did, the passage would contradict his whole philo- 
sophy. This is the more probable from his illustrations, which are drawn from 
circles and ellipses and other mathematical figures. 



64 THE LAW OF CONTINUITY. 

it must be gradual, that a change of position involves the 
intermediate occupation of a continuous series of intermediate 
positions, or a change of colour involves the passage through all 

f I intermediate colours. I do not know any reason for such a 
I principle, unless it be that we only regard qualities in different 
parts of time as belonging to the same thing when they are 
connected by some such continuous series. Jumps from place 
to place and from state to state, according to Leibniz, are 
exactly on a level (G. Ii. 169) ; any a priori reason against the 

' former will apply equally against the latter. Both, he thinks, 
are metaphysically possible, but are condemned by the same 
reason as a vacuum, rest, or a hiatus (G. II. 182), i.e. by what 
he vaguely calls the " order of things " — a sort of metaphysical 
perfection which seems to consist in all that gives pleasure to 

, the metaphysician'. 

I (2) Continuity of cases is the sole form of the law of 

I continuity given in Leibniz's letter to Bayle, on a general 
principle useful in the explanation of the laws of nature 
(D. 33—36; G. iii. 51—55). (This principle states, that when 
the difference of two cases diminishes without limit, the differ- 
ence in their results also diminishes without limit, or, more 
generally, when the data form an ordered series, their respective 
results also form an ordered series, and infinitesimal differences 
in the one lead to infinitesimal differences in the other (D. 33 ; 

I G. III. 52). > This is properly a mathernatical principle, and was 
used as such by Leibniz, with great effect, against Cartesian 
mathematics, especially against the Cartesian theory of impact 
(e.g. G. III. 47). In Mathematics, though it has exceptions in 
cases of what is called instability, it is still in constant use. 

i But in philosophy it seems of no very_^reat momejvt. 

' (3) The third kind of continuity is peculiar to Leibniz, 
and seems destitute either of self-evident validity or of grounds 

i from which it may be proved. That nature makes no leaps, 
which is the general statement of all forms of continuity, is 
held by Leibniz to apply also in the passage from one substance 

1 to another. If two substances differ by a finite difference, there 
must be, according to Leibniz, a continuous series of inter- 

1 Of. G. III. 558 : " There is order in proportion as there is much to remark 
in a multiplicity." 



THE LAW OF CONTINUITY. 65 

mediate substances, each of which differs infinitesimally from f 
the next'. As he often expresses it, there is as little a hiatus, 'i 
or vacuum of forms, as there is a vacuum in space {e.g. G. il. ' 
168). He sometimes pretends {e.g. L. 377 ; N. E. p. 51 ; G. v. I 
49 — 50) to deduce the Identity of Indiscernibles from this 
principle, but such a deduction must be taken only as showing 
how the world can be explained consistently with the Identity 
of Indiscernibles. For continuity asserts that every place in the i 
series is filled, whereas the Identity of Indiscernibles asserts 
that no place is filled twice over. The latter, we shall find, is : 
logically prior to the former. Moreover the latter, as we saw, 
is metaphysically necessary, whereas the former is only demanded 
by order, i.e. is contingent. What Leibniz means to do, in such 
passages, is to point out that, since there are things which only 
differ infinitesimally, and infinitesimal differences are insensible, 
the discovery of things which appear to be indiscernible does 
not make against the denial that they are really indiscernible. 
And this is why Leibniz remarks parenthetically (L. 380 ; N. E. 
52 ; G. V. 51 ) that he has «i priori reasons for his view. 

28. Why Leibniz held that substan_ces form a continuous i 
series, it is difficult to say. He never, so far as I know, offers a 
shadow of a reason, except that such a world seems to him 
pleasanter than one with gaps. I cannot help thinking, how- \ 
ever, that spatial continuity was connected with this form of \ 
continuity. (We shall see hereafter that every monad mirrors 
the world from a certain point of view, and that this point of 
view is often regarded as a spatial point.) Accordingly neigh- i x 
bouring spatial points should give infinitesimally different 
points of view, and therefore, since the mirroring of the universe 
gives the whole of a monad's perceptions, neighbouring points 
in space should be occupied by infinitesimally different monads^. 
There are many objections to this interpretation, which wall 
appear when we come to the relation of the monads to space. 

' Of. N. E. 712 : "All the different classes of beings, whose union forms the 
universe, are in the ideas of God, who knows distinctly their essential grada- 
tions, only as so many ordinates of the same curve, the union of which does 
not allow the placing of others between them, because that would indicate dis- 
order and imperfection." [Guhrauer, Leibnitz: Sine Biographic, Anmerkungen 
zum zweiteu Buche, p. 32.] 

2 Cf. G. IV. 439. 

B. L. 5 



66 POSSIBILITY AND COMPOSSIBILITY. 

I But it will then appear also, I think, that these objections apply 
? I against the whole theory of monads, and cannot, therefore, prove 
that the confusions, involved in the above interpretation of the 
continuity of forms, did not actually exist in Leibniz's mind. 

I 29. The continuity of forms does not assert that all 

■ possible forms are actual. On the contrary, it is vitally 

important to Leibniz's system to maintain that the possible 

I is wider than the actual. < Things are possible when they are 
not self-contradictory ; two or more things are compossible when 
they belong to one and the same possible world, i.e. when they 
may_co^ist.) All possible worlds have general laws, analogous 
to the laws of motion ; what these laws are, is contingent, but 
tjiat there are such laws is n ecessary (G. ii. 51 ; cf also G. II. 
41). Hence two or more things which cannot be brought under 
one and the same set of general laws are not compossible. And 
'fso it is with species. Though actual species form a continuous 

i series, there are other possible species outside the actual series, 
and these, though possible, are not compossible, with those that 

1 exist. Not all possible species, Leibniz says, are compossible, so 
that some species cannot exist. There are of necessity species 
which never have existed and never will exist, not being com- 
patible with the series which God has chosen. There is no gap 
in the order of nature, but no one order contains all possible 
species (N. E. 334; G. v. 286). 

The question of possibility and compossibility is important 

in Leibniz's philosophy, as his solution of the problem of evil 

" I turns on it. It may be well, therefore, to examine the meaning 

I of compossibility in somewhat greater detail. 

I There are, according to Leibniz, an infinite number of 
possible worlds, i.e. of worlds internally free from self contradic- 

' tion. [These worlds all agree in certain respects — i.e. as regards 
the eternal truths — while they differ in others.) The notion of 
an existent is possible when it does not involve a contradiction. 
Any such notion forms part of the notion of some possible 
world. When several notions of possible existents form part of 
the notion of one and the same possible world, they are com- 
possible, for in this case they may all exist (cf G. ill. 573). 
When they are not compossible, then, though each separately 
is possible, yet their coexistence is not possible, 



POSSIBILITY AND COMPOSSIBILITY. 67 

The meaning of compossibility is thus sufficiently plain, i 
But a difficulty remains as regards its application. (For we saw 
that no two contingent predicates of a substance, according to 
Leibniz, are necessarily connected.) Each is necessarily con- 
nected with the notion of the substance, in the sense that, given 
that substance, each predicate follows. (But each separate 
contingent predicate might also have belonged to a different 7 
substance,) and thus no two such predicates are necessarily 
connected with each other. Thus it would seem that any ' 
collection of possible existents must be compossible, since their tJ^'^ 

coexistence cannot be self-contradictory (cf. supra, pp. 19, 20). ' ^%^/ 

This difficulty is evaded by Leibniz by means of the neces- - 1 
sity for some sufficient reason of the whole series. Although 
this or that sufficient reason is contingent, there must be some 
sufficient reason, and the lack of one condemns many series of 
existents as metaphysically impossible. " There were," he says, 
" an infinity of possible ways of creating the world, according to 
the different designs which God might form, and each possible 
world depends upon certain principal designs or ends of God 
proper to itself, i.e. certain free primitive decrees (conceived svb 
ratione possibilitatis), or laws of the general order of this possible 
universe, to which they belong, and whose notion they deter- 
mine, as well as the notions of all the individual substances 
which must belong to this same Universe" (G. ii. 51). This i 
passage proves quite definitely that all possible worlds have 
general laws, which determine the connection of contingents 
just as, in the actual world, it is determined by the laws of 
motion and the law that free spirits pursue what seems best to 
them \ And without the need for some general laws, any two 
possibles would be compossible, since they cannot contradict 
one another. Possibles cease to be compossible only when there 
is no general law whatever to which both conform. What is i 
called the "reign of law" is, in Leibniz's philosophy, meta- 
physically necessary, although the actual laws are contingent. 
If this is not realized, compossibility must remain unin- i 
telligible. 

30. At this point it may be well, for the sake of clearness, 

' This is a point on which, according to Lotze, Leibniz never pronounced. 
(Metofphysics, Book I. Chap. V. § 67.) 

5—2 



■V" 



v^ 



68 POSSIBILITY AND COMPOSSIBILITY. 

I to enumerate the principal respects in which all possible worlds 
agree, and the respects in which other possible worlds might 
I differ from the actual world. For this purpose, since Leibniz 
himself is not very explicit, we have to consider which proposi- 
tions are necessary and which contingent. I shall content 
myself, at present, with stating opinions ; the evidence will be 
given where the various questions concerned are dealt with in 
detail. 
r In the first place, God was free not to create any of the 

•^ possible worlds. Hence even what exists in all of them does 
.. , not exist necessarily. (This applies especially to space, time, 
I and motion.) These are necessary as regards their properties, 
I i.e. as regards the propositions of Geometry and Kinematics, 
! but not as regards their existence. <^God could not have created 
a world in which space and time would be other than in the 
present world, and time, at least, would form part of any 
possible world, while space and motion would form part of any 
world in which there were many substances. All possible 
worlds, again, consist of monads, i.e. of individual substances 
endowed with activity; and in all possible worlds there are 
general causal laws."> But the plurality of substances is not 
necessary ; it would have been possible for God to create only 
one monad, and this one might have been any one of the 
' actual created monads. All that is involved in perception and 
the pre-established harmony, including the existence of other 
substances, is contingent. It would seem, even, that any 
casual selection among the actual monads would give a possible 
world'. But worlds may differ from the actual world, not only 
in number and quantity, but in quality. Other worlds might 
have other laws of motion, and might, if I am not mistaken, 
contain free substances which would not always choose the 
I apparently best. Every causal law, in fact (though not 
! Causality itself), might have been different. 

These seem to be the main points concerning the other 
possible worlds. By keeping them in mind, we obtain a kind 
of hierarchy among Leibniz's principles, as they are successively 

1 This appears not only from the mutual independence of the monads, but 
also from a discussion with Des Bosses concerning the successive days of the 
creation in Genesis : e.g. G. ii. 368, 370. 



POSSIBILITY AND COMPOSSIBILITY. 69 

specialized by the approach to the actual world. The in- 1 
consistencies in his logical doctrine of possibility will be best j ? 
postponed until we come to the proofs of the existence of God. ; 

31. In relation to possibility and corapossibility, Leibniz 
distinguishes several kinds of necessity. There is first meta- ? 
physical or geomejtrical necessity, which alone is strictly called 
necessity. (This is the sort we have hitherto discussed, where 
the opposite is self-contradictory.) There is next hypothe_tical >- 
necess ity, where a consequen ce folio vys with metaphysical neces- 
sity from a contingent premiss. CThus the motions of matter 
have hypothetical necessity, since they are necessary conse- 
quences of the laws of motion, while these are themselves 
contingent.) There is lastly moral necessity, which is the > 
njecessity by which God and the angels and the perfect sage 
cJioose_the_good . The actions of free spirits hold a peculiar 
place in relation to necessity. Not only do their states, in ' 
so far as they are the results of previous states, have only 
hypothetical necessity, but the consequence itself has only 
hypothetical necessity, as involving a psychological law which 
the spirits are not compelled to obey, though they always do 
obey it'. The difficulties in this conception will be discussed ' 
when we come to the problem of Freedom and Determination. 
For the present, it is time to leav e the logical discussions upon | "^ 
which we have been engaged, and proceed to the Philosophy of { 
Matter, from which, by the help of the logic with which we are ] 
now acquainted, Leibniz deduced the doctrine with which ex- j 
positions usually begin, I mean the doctrine of monads. 



1 Cf. D. 170, 171 ; G. iii. 400, 401. 



70 



CHAPTEE VI. 



WHY DID LEIBNIZ BELIEVE IN AN EXTERNAL WORLD ? 

[ 32. I PASS now to an entirely new order of ideas. From 
i questions of Logic — the nature of propositions, the definition of 
substance, how substances must differ if there be many — from 
, these questions I come to questions as to the actual world : 
how can the notion of s ubstance be applied in the world of 
f existe nts ? Is there one substance or many ? What properties 
' have actual substances beyond those involved in the definition 
\ of substance ? And how does this notion serve to explain the 
! difiiculties which the actual world presents to the meta- 
physician ? 
[ In this problem, Leibniz, for reasons which apparently were 
' only historical and psychological, began with matt,er as his 
datum. He would seem, when he first abandoned scholasticism, 
to have turned to Gassendi and Hobbes, to atomism and 
materialism (G. III. 620 ; iv. 209 ; vii. 377 ; iv. 478 and L. 300 
and D. 72 ; G. i. -52 — 4). That he did not remain a materialist 
was due to difficulties which he found in the ordinary con- 
ception of matter. He therefore invented what may be called 
a spiritualistic or idealistic theory of matter: but what his 
f theory started with was still matter. Accordingly, the problem 
with which he began was not : Does matter exist ? But, what 
) is the nature of matter ? In this respect, Leibniz, whose 
ontology begins with Dynamics, which it gradually transforms 
into psychology, was less philosophical than Bishop Berkeley. 
[The question: Does matter exist? is thus one which Leibniz 
! never thoroughly faced. Nevertheless, there are some remarks 



WHY DID LEIBNIZ BELIEVE IN AN EXTERNAL WORLD? 71 

of his, on this question, which may help us to understand his 
position. 

Two short works are, in this respect, peculiarly important. 
The first of these is a letter to Foucher, written in or about 
the year 1676, nine or ten years before Leibniz completed his I 
philosophy (G. L 369 — 374). The second is a paper without date, 
entitled " On the method of distinguishing real from imaginary 
phenomena" (G. vn. 319—322; N. E. 717—720). Though' 
scattered remarks in his later writings seem in agreement with 
these two papers, I can find nothing dated, after his philosophy 
was complete, in which the existence of matter is seriously i 
discussed, and it seems at least possible that Leibniz was only 1 
led to question its existence by the difficulties of the continuum, 
which, in his opinion, the doctrine of monads completely and 
satisfactorily solved. This view is supported by Leibniz's own i 
account of the origin of his views in the Systeme Nouveau^: "At ) 
first, when I had freed myself from the yoke of Aristotle, I took to 
the void and the atoms, for that is the view which best satisfies 
the imagination. But having got over this, I perceived, after 
much meditation, that it is impossible to find the principles of \ 
a real ■wnity in matter alone, or in that which is only passive, 
since it is nothing but a collection or aggregation of parts ad 
infinitum. Now a multiplicity can derive its reality only from - 
genuine units, which come from elsewhere and are quite other 
than mathematical points, which are only extremities of the 
extended and modifications, of which it is certain that the ■ 
continuum cannot be composed. Accordingly, in order to find i 
these real units, I was constrained to have recourse to a real \ 
and animated point," etc. (it would seem that a good many j 
years elapsed between Leibniz's discovery that mere matter 
involved the insoluble difficulties of the continuum, and his 
invention of monads as real units by which the continuum was 
rendered discrete I) This theory, at any rate, accounts both for 
his views, and for his manner of exposition, much better than 
any other theory with which I am acquainted. But it is time 
to examine Leibniz's actual words. 

1 L. 300; D. 72; G. iv. 478; of. also ArcUv. fur Gesch. der Phil. i. 577 [L. 
351—2]. 

2 See Chapter IX. 



72 WHY DID LEIBNIZ BELIEVE IN AN EXTERNAL WORLD? 

33. Leibniz does not clearly distinguish two totally dif- 
ferent questions, namely, (1) why admit a world other than 
ourselves ? (2) granted such a world, how shall we distinguish 
true perceptions from hallucinations 1 The latter, as the title 
indicates, is the main question discussed in the undated paper 
above quoted. This is not a fundamental question, and Leibniz 
answers it in the usual way — mutual consistency, and success 
in prediction, he says, are the best tests. He proceeds, how- 
ever, to a radically unphilosophical remark on the first question. 
"Although the whole of this life were said to be nothing but a 
dream, and the visible world nothing but a phantasm, I should 
call this dream or phantasm real enough, if, using reason' well, 
we were never deceived by it" (N. E. 718 — 9 ; G. vii. 320). In 
this passage, the unduly practical nature of Leibniz's interest 
in philosophy very plainly appears. He confesses, both here, 
and in many other passages, that there is no " exact demon- 
stration " that the objects of sense are outside us, and that the 
existence of the external world has only moral certainty '. To 
obtain even this, he requires first the existence of God, which 
has absolute certainty. (He says, for example : " That there 
should exist only one substance " (created substance, he seems 
to mean) " is among those things which are not conformable to 
the divine wisdom, and thus do not happen, although they 
might happen" (G. II. 307).') And in one early passage (G. I. 
372 — 3, ca. 1676), he actually suggests Berkeley's philosophy. 
All we know for certain, he says, is that our appearances are 
connected inter se, and that they must have a constant cause 
external to us ; but there is no way of proving this cause to be 
other than God. Yet, though he seems never to have found 
arguments against this admission, he so far forgot his early 
unresolved doubts, that, when Berkeley's philosophy appeared, 
Leibniz had no good word for it. "The man in Ireland," he 
writes, "who impugns the reality of bodies, seems neither to 
give suitable reasons, nor to explain himself sufficiently. I 
suspect him to be one of that class of men who wish to be 
known by their paradoxes" (G. ii. 492). 

If any arguments for the existence of matter were to be 
found in Leibniz, they would evidently depend upon the ex- 

' N. E. 318, 422, 719; G. v. 275, 35S— 6; vii. 320—321; i. 373; ii. 378, 502. 



WHY DID LEIBNIZ BELIEVE IN AN EXTERNAL WORLD ? 73 

istence of God, by which solipsism is destroyed. The Cartesian j 
argument, however, which rests on the assertion that, if there | 
were no matter, God would be a deceiver, is definitely rejected ' 
by Leibniz. "The argument by which Des Cartes seeks to 
demonstrate the existence of material things is weak. It would 
have been better therefore not to try" (D. 58; G. iv. 366). 
God might, he says, have excellent reasons for deceiving us, 
and, in any case, the deception could be undone by our own 
reason (D. 58 ; G. IV. 367 ; I. 373 ; v. 275 ; N. E. p. 318). 

There is, it is true, a kind of pantheistic argument, ac- 
cording to which our view of the world is part of God's view, 
and therefore has the same truth as belongs to God's per- 
ceptions. " God... regards all the aspects of the world," Leibniz "^""''' 
says, "in all possible ways...; the result of each view, as if 
seen from a certain place, is a substance expressing the uni- 
verse from this point of view, if God sees fit to make his 
thought effective and produce this substance. And since God's 
view is always veritable, our perceptions are so too ; but it is 
our judgments, which are from us, that deceive us" (G. IV. 
439). This whole passage, however, is so extreme an example | 
of Leibniz's pantheistic tendencies, as to be scarcely consistent 1 
with his usual monadism. He can hardly, therefore, have j 
relied upon such an argument to any great extent. 

The only other positive argument is one no better than 
that which is commonly urged for life on other planets. " We 
judge with the greatest piobability," he says, " that we do not 
exist alone, not only by the principle of the Divine Wisdom, 
but also by that common principle which I always inculcate, 
that nothing happens without a reason, nor does a reason 
appear, why we alone should be preferred to so many other 
possibles"(G. n. 502)'. 

The ground upon which Leibniz seems to have mainly ' 
relied, in this question, is the same as that which led him to 
deny a vacuum, namely, that t he more existence there is, the 
laett^r. (cf. D. 102, 103; L. 340, 341 ; G. vii. 303, 304). This 
is the principle of metaphysical perfection, which I shall discuss 
in connection with his Ethics. It led Leibniz to think that . 
there must be as many monads as possible, and that there 

1 Of. G. II. 516. 



74 WHY DID LEIBNIZ BELIEVE IN AN EXTERNAL WORLD? 

must, therefore, be an infinity of substances other than him- 
^ j self. But historically and psychologically, I think, Leibniz 

1 started with matter and space in a purely common-sense spirit. 
The reason that a problem arises for him is, that by criticism 
of these notions he transformed them into something quite 
different, namely, unextended substances and their perceptions. 
But having arrived at the subjectivity of space, he did not, like 
Kant, confine knowledge to experience, and render all d priori 

I knowledge really self-knowledge. He did not perceive that 
the denial of the reality of space compels us to admit that we 

I know only phenomena, i.e. appearances to our minds. That 
Kant was able to assume even an unknowable thing-in-itself 
was only due to his extension of cause (or ground) beyond 
experience, by regarding something not ourselves as the source 
of our perceptions. This, which was an inconsistency in Kant, 
would have been a sheer impossibility to Leibniz, since he held 
perceptions to be wholly due to ourselves, and not in any sense 
^ j caused by the objects perceived. The ordinary grounds for 

I assuming an external world were thus destroyed by Leibniz, and 

' I cannot discover that anything very solid was put in their place. 
^ j The existence of other substances, besides God and our- 

i selves, is therefore only probable : it has only a moral certainty. 
This remark applies, consequently, to all existential propo- 
sitions derived from the theory of matter, i.e. to the whole 
doctrine of monads, in so far as this asserts the actual existence 
of many monads. It is a pity that Leibniz did not devote 
more attention to this fundamental question, that he did not 
make himself the critic rather than the commentator of 

' common sense. Had he done so, he might have invented some 
more satisfactory theory of space than one which, while based 

! upon a common-sense assumption of its reality, arrives, on that 

' very basis, at a complete denial of that reality. I have brought 

out this presupposition now, as the following Chapters will, with 

Leibniz, start from a common-sense belief in the reality of matter. 

1 Cf. L. 323 ; D. 86; G. iv. 495: "I am asked whence it comes that God does 
not think it enough to produce all the thoughts and modifications of the soul, 
without these useless bodies, which the soul, it is said, can neither move nor 
know. The answer is easy. It is, that it was God's will that there should be 
more substances rather than fewer, and He thought it right that these modifica- 
tions should correspond to something outside." 



^■' n r 






OHAPTEE VII. 






THE PHILOSOPHY OF MATTER. 



(a) J.S iAe outcome of the principles of Dynamics. 

34. The word matter is, in philo^phy, the name of a 
proljlem. Assuming that, in perception, we are assured of the 
existence of something other than ourselves — an assumption 
which, as we saw in the last chapter, Leibniz made on very 
inadequate grounds — the question inevitably arises: Of what 
nature is this something external to ourselves? Cin so far as it 
appears to be in space, we name it matter (cf. G. iv. 106). 
Our problem is, then, what is matter ?)how are we to conceive 
that which, in perception, appears as spatial and as other than 
ourselves? It was the attempt to answer this question, on 
the basis of the logic which we have already examined, that 
led Leibniz to the doctrine of monads. In this and the three 
succeeding chapters, I shall endeavour to follow the same course 
as Leibniz followed. I shall intersperse criticisms where they 
seem called for, but the chief criticism of Leibniz's procedure 
is, that he never examined its starting-point, the assumption, 
namely, that there is something other than ourselves to be per- 
ceived. (The general trustworthiness of perception is a premiss 
of Leibniz's philosophy, but a faulty premiss, even if it be true, 
since arguments may be adduced for or against it.) 

35. Before I enter on any detail as to Leibniz's theory of 
Dynamics, I must warn readers that he uses the words matter 
and hody in at. least five different senses. (These are not con- 
fused in his own thinking, and are often distinguished in his 
writings.) At the same time, the words are often employed 
without any indication, except what the context provides,. as to 



-H' 



tVli. 



76 THE PHILOSOPHY OF DYNAMICS. 

the sense to be attached to them, and this adds greatly to the 

difficulty of understanding Leibniz's theory of matter. Of 

these five senses, two are prior to the theory of monads, and 

I three are subsequent. (There is, in the first place, the dis- 

yyu I tinction of primary and secondary matter; and th is distinction 

I i s one thing in Dyna mics, and ano ther in the theory_of. monads. 

Thus we have four meanings of matter. In addition to these, 

there is the organic body of a monad, which consists of other 

I monads subordinated to it.^ It is the object of Leibniz's theory 

! to transform primary and secondary matter as they occur in 

j Dynamics, into primary and secondary matter as they occur in 

I the theory of monads. At the same time, since the first pair 

are data, while the second pair are results, it is important to 

distinguish them, and Leibniz's correctness may be tested by 

examining how far his criticism of dynamical matter does 

justify the transformation. 

The five meanings, then, to be definite, are as follows. 
[^ (1) There is primary matter as that which, according to 
Leibniz, is p resupposed by extension . Extension, as 
we shall see in the next chapter, is regarded by him 
as mere repetition. That which is repeated, taken 
per se, is materia prima. This is purely p assive. 
(2) There is secondary matter as it occurs in Dynamics, 
that is, matter^ endowed with, force- The further 
explanation of these two meanings will occupy the 
s- remainder of this chapter. ~\ 

' (3) There is primj,ry matter as an elemeiit in the nature 
! of every created monad. (In this sense, it is equiva- 

lent to passivity, or confusedness of perception.^ 

(4) There is secondary matigr as an aggrggate of monads, 
or mag.s : this is a mere aggregate with only an 
accidental unity. 

(5) There is the organic body of a monad, i e. the collection 
of monads which it dominates, and to which it gives 
a more than accidental unity (G. ii. 252; N.E. 
p. 722 and G. vii. .501). 

The transformation of the first pair of meanings into the 
second pair constitutes the proof of the doctrine of monads, 
and will occupy the next three chapters. The second and 



/ 



THE PHILOSOPHY OF DYNAMICS. 77 

fourth senses are often called mass or body, the fifth with the 
dominant monad is often called corporeal substance; without 
the dominant monad, it is called the organic body, or simply 
the body, of the dominant monad. But there is little regularity 
in Leibniz's use of all these words, and the meaning must 
generally be gathered from the context. 

36. Leibniz's theory of Dynamics was framed in conscious 
opposition to Des Cartes. ])es Cartes held that the essence of 
matter is extension, that the quantity of motion in the universe 
is constant, and that force is proportional to quantity of motion. 
Leibniz, on the contrary, proved that the essence of matter is 
not extension, that the total quantity of motion is not constant, 
but that, what Des Cartes did not know, the quantity of 
motion in any given direction is constant. (^He also believed 
himself to have proved that Dynamics required, as an ultimate 
notion, the conception of force, which he identified with the 
activity essential to substance.^ Des Cartes and the Cartesians 
measured force by quantity of motion, from which they seem 
scarcely to have distinguished it. Leibniz, on the contrary, 
believing force to be an ultimate entity, and holding as an 
axiom that its quantity must be constant, introduced a different 
measure of it, by which it became proportional to what is now 
called energy. On this question of the true measure of force, a 
famous controversy arose, which was distinguished by the fact 
that it divided Voltaire and the Marquise du Chatelet, and 
that it formed the subject of Kant's first published work^ 
This controversy seems to modern mathematicians to be mere 
logomachy. To Leibniz and his contemporaries it seemed 
something more, because force was supposed to be an ultimate 
entity, and one whose quantity, like that of mass, must be 
constant. 

37. That the essence of matter is not extension, is a 
proposition on which Leibniz loves to dwell. He seems to 
have discovered this proposition at least as early as 1672", so 

' Gedanken iiber die wahre Schdtzung der lebencligen Krdfte, 1747. Ed. Hart. 
Vol. I. 

^ This results e.g. from his saying that he has geometrical proofs of the 
existence of a vacuum (G. i. 58). That Leibniz was aware of the fact that a 
vacuum is inconsistent with the view that the essence of matter is extension, 
appears also from G. i. 321. Again in a letter to Antoine Aruauld, written 



78 THE PHILOSOPHY OF DYNAMICS. 

that it was probably one of the sources of his innovations. 
The proof of the proposition is about as thorough as it could 
be. It is derived (1) from the nature of extension, (2) from 
the nature of the extended, or materia prima, (3) from the fact 
that even materia prima, though not mere extension, is an 
abstraction, requiring to be supplemented by force or activity. 
The argument from the nature of extension, with its conse- 
quences, I leave for the next chapter ; the other two arguments 
must now be given. Let us begin with the definition of 
materia prima as it occurs in Dynamics. 

38. Materia prima is defined by what Leibniz calls re- 
sistance. This, he says, does not consist in extension, but is 
the principle of extension (G. II. 306), that is, it is the quality 
in virtue of which bodies occupy places. Resistance, again, i 
involves two distinct properties, impenetrability or antitypia, 
and resistance (in the narrower sense) or inertia (G. il. 171)'. ( 
I These two properties of materia prima might be defined as 
I (1) the property of bodies in virtue of which they are in places 
I (G. VII. 328), (2) the property in virtue of which they resist 
! any effort to make them change their places. Passive force, 
Leibniz says, is a resistance, by which a body resists not only 
penetration, but also motion, so that another body cannot come 
into the place of the first unless the first gives way, and it does 
I not give way without retarding the other. Thus there are two 
resistances or masses, impenetrability and inertia. These are 
uniform everywhere, and therefore proportional to extension 
(G. IV. 395 ; G. M. vi. 100 and N. E. p. 701). Inertia is spoken 

probably at the end of 1671 or the beginning of 1672, Leibniz says (G. i. 72) 
that he has proved, among other things, "that the essence of body does not 
consist in extension, since empty space must be different from body, and yet is 
also extended"; further "that the essence of body consists rather in motion." 
Cf. G. IV. 106 (1669) : " The definition of a body is that it exists in space.'' 
Also lb. 171 (1670). See Selver, Entwickelungsgang der Leibniz' schen Monaden- 
lehre, p. 49. Leibniz appears to have been led to this discovery by the search 
for a philosophical theory of the Eucharist. The Cartesian doctrine, that the 
essence of matter is extension, was found by him to be inconsistent with both 
transubstantiation and consubstantiation. See Guhraner, Leibnitz : Eine Bio- 
graphie, Vol. i. p. 77. 

' The use of resistance in two senses, (1) as the whole essence of materia 
prima, (2) as inertia only, is very tiresome, and greatly confuses Leibniz's 
exposition. 



THE PHILOSOPHY OF DYNAMICS. 79 

of as a passive force, a somewhat difficult phrase, which we 
shall find to be equivalent to what, in the theory of monads, is 
called passivity simply. Thus Leibniz says (ib.) : " Again to 
SvvafiiKov or power in body is twofold — passive and active. 
Passive foi'ce properly constitutes matter or mass, the active 
constitutes ivTeKexeta or form. Passive force is that very 
resistance by which body resists not only penetration, but also 
motion." And passive force, as we shall find with active force 
also, " is twofold, either primitive or derivative. And indeed the 
primitive force of enduring or resisting constitutes that very 
thing which is called materia prima, rightly interpreted, in the 
schools, by which it happens that body is not penetrated by 
body, but forms an obstacle to it, and is endowed also with a 
certain laziness, so to speak, that is, repugnance to motion, and 
does not indeed suffer itself to be set in motion unless by the 
somewhat broken force of the active body. Whence afterwards 
the derivative force of enduring variously exhibits itself in 
secondary matter" (N. E. p. 672—3; G. M. vi. 236). Re- 
sistance, Leibniz says, is not merely not changing without 
cause, but having a force and inclination to retain the actual 
state and resist the cause of change. Thus in impact (which 
he has always in his mind in the mathematical discussion of 
materia prima), when one body is at rest, the impinging body 
loses some of its velocity in starting the other, and the other, 
when started, moves more slowly than the first did'. Resistance 
in this sense, he asserts, is not metaphysically necessary 
(G. II. 170). 

(As part of an actual theory of Dynamics, the above analysis 
is antiquated, j But philosophically, it is easy to see what is 
meant by the two elements of materia prima. Not only is it 
impossible for one body to come into the place occupied by 
another, unless that other gives way, and moves into a new 
place, but also some of the first body's motion is absorbed by 
the second body, or some effort is required to cause the second 
body to abandon its place. The importance of the doctrine ' 
lies, as we . shall afterwards see, in the connection with the 
materia prima of each monad. A difficulty, which I think is a 
bare inconsistency, is introduced by the statement that materia 
1 See L. 352—3; N. E. 678 ; G. M. vi. 240. 



80 THE PHILOSOPHY OF DYNAMICS. 

prima, as an element in each monad, is metaphysically neces- 
sary (G. II. 325). It is more consistent with Leibniz's philo- 
sophy, I think, to hold both necessary than to hold both 
contingent ; particularly as the necessity of the one is declared 
much more emphatically than the contingency of the other. 

Neither of the properties of materia prima can be deduced 
from mere extension. That this is true of impenetrability, 
follows from the simple consideration that place, though ex- 
tended, is not impenetrable (G. iii. 453). As regards inertia, 
Leibniz points out that, if bodies were wholly indiflferent to 
rest and motion, a big body could be set in motion by a small 
' one without any loss of velocity, whereas what is really con- 
! served is momentum, which involves mass. But for inertia, we 
should have action without reaction, and no estimate of power 
could be made, since anything might be accomplished by any- 
thing (L. 353 ; N. E. 678 ; G. M. vi. 241). Even if matter, 
then, were purely passive, Des Cartes' theory, that the essence 
of matter is extension, would be mistaken. 

39. But this is still more evident when we pass to materia 
secunda, i.e. to matter as active and endowed with force. The 
doctrine of force is closely connected with every part of 
Leibniz's philosophy — with the notion of contingent truths^, 
with the conception of substance as the source of all its 
predicates^, with the plurality of independent causal series 
(D. 60, 61 ; G. iv. 369), with the psychical nature of all 
substances', and with the whole theory of activity, liberty and 

' "You are right in judging that (Dynamics) is to a great extent the founda- 
tion of my system ; for it is there we learn the difference between truths whose 
necessity is brute and geometrical, and truths which have their source in fitness 
and final causes" (G. iii. 645). 

2 "I am not astonished that you find insurmountable difliculties where you 
seem to assume a thing so inconceivable as the passage of an accident from one 
subject to another; but I see nothing which compels us to an assumption which 
is scarcely less strange than that of the scholastics of accidents without a sub- 
ject" (N. E. p. 233, G. V. 208); in answer to Locke's difficulties concerning 
impact. Cf. also D. 124; G. iv. 515: in a series of impacts, "each ball, when 
repelled from the next one impinging on it, is set in motion by its own force, 
viz. its elasticity.'' 

3 "We see also, that thought, being the action of a thing on itself, cannot 
happen in figures and motions, which can never show the principle of a truly 
internal action" [G. iii. 69]. Such a principle, however, ie found in force. 



THE PHILOSOPHY OF DYNAMICS. 



81 



determination. It is a central point in Leibniz's philosophy, 
and was by him recognized as such. Force is said to be prior 
to extension (N. E. 671 ; G. M. vi. 235), and to be the true 
ground for inferring the plurality of substances (G. II. 372). 
In so far as force is the same as activity, we have already 
considered it. What we have now to examine, is the way in 
which Leibniz developed the idea of force from Dynamics. 

Leibniz discovered the conservation of momentum, and | 
believed himself to have discovered another law, the conserva- 
tion of Vis Viva, both of which were unknown to Des Cartes 
(D. 88 ; L. 327 ; G. iv. 497). He was thus able theoretically- 
assuming perfectly elastic impact to be ultimately the only 
form of dynamical action — to determine completely the course 
of any motion, and to disprove, if the validity of his Dynamics 
was allowed, the possibility, admitted by Des Cartes, of a direct 
action of mind upon matter. Des Cartes had supposed that, 
though the quantity of motion is constant, its direction may be 
altered by a direct action of the mind upon the animal spirits. 
Had he known, Leibniz says, that the quantity of motion in 
every direction is constant, he would probably have discovered 
the pre-established harmony (D. 164; G. VI. 540); for he 
would have seen that an interaction between mind and matter 
is impossible. Why he should not have been led to the views 
of Geulincx or of Spinoza, which Leibniz does not mention, it 
is very difficult to see. That Leibniz was not led to occasional- | 
ism, or to Spinoza's theory that the mind is the idea of the 
body, was due to his conception of force, which led him to 
regard every piece of matter^ — or rather every collection of the 
real substances whose appearance is matter — as an independent 
source of all its own changes. 

40. The necessity of force is variously deduced. Much of 
the argument — especially when it assumes the form of a 
polemic against the Cartesians — depends, as Wundt has pointed 
outs upon the axiom that the cause must be equal to the effect. 
The two measures of force only give the same result in the 
case of equilibrium, i.e. in Statics; and Leibniz attributes the 



^. 



1 Die physikalischen Axiome und ihre Beziehung man GausaVprincip, Erlangen, 
1866, p. 60 fl. Many valuable observations on Leibniz's Dynamics are contained 
in this vrork. 



82 THE PHILOSOPHY OF DYNAMICS. 

persistence of the Cartesian measure to the fact that people 
have devoted an undue share of attention to Statics as opposed 
to Dynamics (N. E. 675; G. M. vi. 239). Since the quantity of 
motion is not conserved (as Des Cartes had falsely assumed), the 
true causes and effects cannot be motions. Motion in a given 
direction might have been substituted, if purely mathematical 
considerations had been alone employed. But for an ultimate 
physical entity, Leibniz desired some one unique quantity, 
which had a constant sum in any independent system ; and 
this he believed himself to have found in Vis Viva, i.e. the 
mass multiplied by the square of the velocity. Statics and 
Dynamics are to be deduced from the law " that the total effect 
must always be equivalent to its full cause." " As in Geometry 
and numbers," he explains, "through the principle of the 
equality of the whole to all its parts. Geometry is subjected to 
an analytical Calculus, so in Mechanics, through the equality of 
the effect to all its causes, or of the cause to all its effects, we 
obtain certain equations, as it were, and a kind of mechanical 
Algebra by the use of this axiom'." In a thorough discussion 
of the principles of Dynamics, it would be necessary to examine 
this supposed law, but here it is sufficient to point out its influ- 
ence on Leibniz's views. For, as he himself appears to recognize 
{Archiv, loc. cit), it belongs more to the mathematics than to 
the philosophy of the subject". I therefore pass now to the 
more strictly philosophical arguments. 

While Leibniz was crossing from England to Holland, on 
his way to visit Spinoza, he composed a highly interesting 
dialogue on the difficulties arising from the continuity of 
motion". At the end of this dialogue he remarks: "Here I 
have considered the nature of change and the continuum, in so 
far as they belong to motion. It remains to consider, first the 
subject of motion, that it may appear to which of two bodies, 
which change their relative situation, the motion is to be 

' L. 354 ; Archiv fur Geschichte der Philosophie, i. p. 576. The same maxim 
was employed by Leibniz in arguing with Spinoza in 1676 against Des Cartes' 
laws of motion : see L. p. 10, and Fouoher de Careil, R&futation inSdite de 
Spinoza, p. Ixiv. 

2 Though iu a letter to Bayle he speaks of it as a "wholly metaphysical 
axiom " (G. m. 46). 

2 See Archiv f. Geschichte der Phil, i. pp. 211 — 5, 



THE PHILOSOPHY OF DYNAMICS. 83 

ascribed; secondly, the cause of motion, or motor force" 
(p. 215). The question of the continuum I leave for a later 
chapter ; the other two were solved together, in Leibniz's 
opinion, by the notion of force which he afterwards gained. 

That motion requires force, or a principle of change, in the 
moving body, was deduced by Leibniz partly from abstract 
metaphysical reasons, partly from the relativity of motion, and 
partly from the so-called law of inertia, i.e. the law that every 
body persists in any motion which it has acquired, except in so 
far as it is hindered by outside caiises. I shall begin with the 
last of these arguments. 

The law of inertia states, on the one hand, that a body will 
not of itself begin a motion, but that, on the other hand, " body 
retains of itself the impetus which it has once acquired, and 
that it is constant in its levity, or has an endeavour to perse- 
vere in that very series of changes which it has entered upon " 
(D. 120; G. IV, 511). A moving body is not merely succes- 
sively in different places, but is at each moment in a state of 
motion ; it has velocity, and differs, in its state, from a body at 
rest (D. 122; G. IV. 513). But this involves some effort to 
change its place, whence the next state follows of itself from 
the present. Otherwise, in the present, and therefore in every 
moment, a moving body would differ in no way from one at 
rest (lb.). This argument is valid, I think, as against those 
who, like Clerk Maxwell (Matter and Motion, Art. XLI.), en- 
deavour to represent Newton's First Law as a self-evident 
truth. Leibniz recognizes that, in a uniform rectilinear motion, 
a body undergoes a series of changes, although its velocity is 
unchanged. He infers that, since this series of changes is 
possible without external influence, every body must contain in 
itself a principle of change, i.e. force or activity, by means of 
which a meaning is given to a state of change. But this 
involves the continuity of change, concerning which we are 
faced with those very difficulties to evade which, as regards 
space, was a main purpose of the doctrine of monads. Accord- 
ingly, in other places, where Leibniz is thinking of the diffi- 
culties of the continuum, he holds all change to be discrete 
once even asserting that motion is a continual transcreation'. 
1 G. II. 279. Cf. the dialogue alluded to above, Archiv, Vol. i. p. 212 fl. 

6—3 






84 THE PHILOSOPHY OF DYNAMICS. 

This is an instance of the vacillation into which, as we shall see 
in the next two chapters, Leibniz was led by his refusal to 
admit the antinomy of infinite division. 

41. The most important dynamical argument in favour of 
force is connected with the relativity of motion. On this point, 
Leibniz's views present some suggestion of a vicious circle. He 
seems sometimes to argue that, because force is something real, 
it must have a subject, and be an attribute, not a mere rela- 
tion ; whence it follows that, in a change of relative situation, 
the cause of change can be apportioned between the bodies, thus 
giving a sense to absolute motion (e.g. G. M. ii. 184). But at 
other times, he argues that some real change, not merely 
relative, must underlie motion, and can only be obtained by 
means of force {e.g. D. 60, 61 ; G. iv. 369). This argument is 
interesting, both on account of its difference from the analogous 
arguments by which Newton proved the need of absolute space, 
and by the fact that Dynamics, at the present day, is still 
unable to reconcile the relativity of motion with the absolute- 
, ness of forced In every motion, Leibniz says, the motion per 
se gives a mere change of relative situation, and it is impossible 
to say which body has moved, or whether both have moved. 
In order to be able to say this, we require to know in which is 
the cause of the change of relative situation. This cause we 
call force {lb.). " When formerly," he says, " I regarded space 
as an immoveable real place, possessing extension alone, I had 
been able to define absolute motion as change of this real space. 
But gradually I began to doubt whether there is in nature 
such an entity as is called space ; whence it followed that a 

doubt might arise about absolute motion It seemed to 

follow that that which is real and absolute in motion consists 
not in what is purely mathematical, such as change of neigh- 
bourhood or situation, but in motive force itself; and if there 
is none of this, then there is no absolute and real motion 

' I cannot here undertake to give the proof of this assertion. It depends 
upon the fact that, if the laws of motion are to apply, the motion must be 
referred, not to any axes, but to what have been called kinetic axes, i.e. axes 
which have no absolute acceleration. See Newton, Principia, Scholium to the 
eighth definition. Contrast, in Clerk Maxwell's Matter and Motion, Arts, 
xvni, ov. 



THE PHILOSOPHY OF DYNAMICS. 85 

Accordingly I found no other Ariadne thread to lead me out of 
this labyrinth than the calculation of forces, assuming this 
metaphysical principle, that the total effect is always equal to 
its complete cause " (L. 353 ; Archiv, i. p. 580). 

On this question Leibniz's position, unlike Newton's, is, I ' 
think, full of confusion. On the one hand, space is wholly 
relational ; hence motion is not a change of absolute position, 
but merely a change of relative situation. Now a change of 
relative situation is necessarily reciprocal, and hence Leibniz is 
led to the equality of action and reaction (N. E. 689 ; G. M. vi. 
251 — 2). But in order to give any meaning to action, he has 
to forget the relativity of motion, and consequently to do away 
with the need for an equal reaction. He and Huygens agree, ! 
as against Newton, that the phenomena of circular motion give 
no more indication as to absolute motion than do those of 
rectilinear motion, though Huygens has the honesty to confess 
that he has not examined Newton's grounds (G. M. il. 177, 
184 — 5, 192). The Copernican hypothesis, Leibniz says, anti- 1 
cipating Mach, is simpler, not truer, than the other (N. E. 685 ; j 
G. M. VI. 248). But he nevertheless holds that, by means of I 
force, some meaning may be given to the statement that, in 
a change of relative situation, one body has moved and not the 
other. " As for the difference of absolute and relative motion," 
he says, " I think that if the motion, or rather the motor force 
of bodies, is something real, as it seems that one must recog- 
nize, it is necessary that it should have a subject I agree 

that the phenomena could not furnish to us (or even to the 
angels) an infallible reason for determining the subject of 
motion or of its degree ; and that each can be conceived apart 

as being at rest But you will not deny (I believe) that 

in truth each has a certain degree of motion, or, if you will, of 
force ; in spite of the equivalence of hypotheses. It is true I 
draw from it this consequence, that there is in nature some- 
thing besides what Geometry can determine in it " (G. M. ii. 
184). This, he says, is not the least of his reasons for recog- 
nizing force. Again he says, even more explicitly: "I find 
nothing in the eighth definition of the mathematical principles 
of nature, or in the scholium belonging to it [the scholium in 
which Newton explains the need of absolute space, time and 



86 THE PHILOSOPHY OF DYNAMICS. 

motion] that proves, or can prove, the reality of space in itself. 
However, I grant there is a difference between an absolute true 
motion of a body, and a mere relative change of situation with 
respect to another body " (D. 269 ; G. vii. 404). But it must 
be evident that, if position is relative, absolute motion is mean- 
ingless. The two cannot possibly be reconciled. Leibniz, like 
Newton, rightly perceived that Dj'naraics requires us to distin- 
guish, in a change of relative situation, the proportion in which 
accelerations are shared between two bodies. He was also 
right in maintaining that, on a geometrical or kinematical 
view, such a distinction cannot be practically effected. But 
Geometry does not show the distinction to be meaningless, 
and if it did. Dynamics could not make the distinction. Thus 
it would seem that Newton was right in inferring, from Dy- 
namics, the necessity of absolute space. When I come to the 
theory of space, I shall maintain that even Geometry requires 
this, though only metaphysically, not, like Dynamics, for em- 
pirical reasons also. 

As this point is important, it may be well briefly to repeat 
the arguments which show the relativity of motion to be incon- 
sistent with the absoluteness of force. " As regards Physics," 
Leibniz says, " it is necessary to understand the nature of force, 
a thing entirely different from motion, which is something 
more relative. This force is to be measured by the quantity of 
its effect " (D. 39 ; G. ii. 137). But the objection which here 
arises — an objection unavoidable on any relational theory of 
space — is, that the effect can only be measured by means 
of motion, and thus the pretended escape from endless relativity 
breaks down. A new objection applies to another statement, 
in which Leibniz endeavours to prove that motion is not purely 
relative. " If there is nothing in motion but this respective 
change," he says, " it follows that no reason is given in nature 
why motion must be ascribed to one thing rather than to 
others. The consequence of this will be that there is no real 
motion. Therefore in order' that a thing may be said to be 
moved, we shall require not only that it change its situation in 
respect to others, but also that the cause of change, the force 
or action, be in it itself" (D. 61 ; G. iv. 369. Of also D. 269 ; 
G. VII. 404). This endeavour to establish absolute motion is. 



THE PHILOSOPHY OF DYNAMICS. 87 

in the lirst place, wholly inconsistent with Leibniz's theory of 
space. Newton, from somewhat similar arguments, had rightly 
deduced the necessity of absolute position ; Leibniz, who on 
many mathematical points was less philosophical than Newton, 
endeavoured to save absolute motion, while strenuously denying 
absolute position (cf. D. 266; G. vii. 401—2). But further, 
the theory is inconsistent with the nature of monads. Let us 
suppose two bodies A and B, which change their relative 
situation owing to the force in B. Since A mirrors the uni- 
verse, a change will happen in A when B moves. Hence if the 
force resided only in B, B would cause a change in A, contrary 
to the theory that monads do not, interact. Hence we must, in 
every case of a relative change of situation, place a force in 
both bodies, by which the change is to be effected. Thus we 
shall lose that power of discrimination which force was supposed 
to provide. This argument could only be evaded by the denial 
that monads have anything corresponding to position in space, 
a denial which Leibniz often attempted, but which, as we 
shall see later, would have destroyed the only ground for his 
monadism. 

42. Leibniz's deduction of force as a means of escaping | 
from the relativity of motion is thus fallacious. Motion, in its 
own nature, is or is not relative, and the introduction of force j 
can make no difference to that nature. It remains to examine '< 
the metaphysical grounds for the notion of force. In so far as 
these are the same as those for activity in general, they have 
been already dealt with. But others are derived from the con- 
tinuity of motion, and these must now be set forth. 

"We have elsewhere suggested," Leibniz says (N. E. 671; ] 
G. M. VI. 235), "that there is in corporeal things something 
besides extension, nay, pnor to^extensioij, namely the force of 
nature everywhere implanted by its Author, which consists," not 
in the simple faculty with which the schools seem to have been 
content, but is provided, besides, with a tendency (conatu) or 
effort, which will have its full effect unless impeded by a 
contrary tendency. HThis effort often appears to the senses. 
and in my judgment is known everywhere in matter by the 
reason, even when it does not appear to the sense. But even if 
we are not to assign this force to God through a miracle, it is 



88 THE PHILOSOPHY OF DYNAMICS. 

certainly necessary that it be produced in the bodies them- 
f selves, nay that it constitute the inmost nature of bodies, since 
I to act is the mark of substances, and extension means nothing 
else than the continuation or diffusion of the already presup- 
> posed... resisting substance, so far is it from being able itself to 
constitute the very essence of substance. Nor is it relevant that 
every corporeal action arises from motion, and motion itself 
does not exist unless from motion.... For motion, like time, 
never exists, if you reduce the thing to aKpL^eia, because it 
never exists as a whole, since it has not co-existing parts. And 
nothing at all is real in it, except that momentar}' property, 
which must be constituted ]3y a force striving for change." 
This is the old argument of Zeno, suggested also in the dia- 
logue written for Spinoza {Archiv, I. p. 213), and in many 
other passages. Motion is change of position ; but at any one 
instant the position is one and only one. Hence at every 
instant, and therefore always, there is no change of position and 
no motion. Leibniz thought, however, what the Calculus was 
likely to suggest, that the momentary increment was real in 
some way in which the whole sum of increments was not real ', 
and hence force was called in to supply some reality other 
than motion, out of which motion might be supposed to spring. 
"Force," he says, "is something truly_real, even in created 
substances; but space, time and motion ^partake of the nature of 
mental, entities.( eras rationis) and are true and real, not of them- 
selves, but since they involve divine attributes" (N. E. p. 684; 
G. M. VI. 247). And again, " Only force, and thence nascent 
effort, exists in any moment, for motion never truly exists" 
(N. E. p. 689 ; G. M. vi. 252). What Leibniz designs to effect, 
by this doctrine, is, as with activity in general, the reduction of 
a relation to a quality. Motion is doubly a relation — first, as 
between successive moments, and secondly, as between bodies 
in different places. Both relations were to be reduced by 
means of force. A state of motion is distinguished from a 
state of rest, at each instant of the motion, by the presence 
of force, which, in the last analysis, is akin to desire. By 
this means, not only are the difficulties of the temporal con- 
tinuum supposed to be overcome (L. 351 ; Archiv. i. 577), but 
' Cf. Cohen, Injinitesimalmethode, p. 15. 



'vt. ^i 



THE PHILOSOPHY OF DYNAMICS. 89 

also, when two bodies change their relative situation, we can 
enquire whether one or both contains force, and thus assign 
an appropriate state of motion to each. 

43. The objections to this view of force will appear more 
clearly from an examination of its application to the case of 
impact, and of the attempt to establish dynamically a plura- 
lity of causal series. We shall then find, if I am not mistaken, i 
that t he re lation of Leibniz's Dynamics, to his Metaphysics is 
ho peless ly confused, and that the one cannot stand while the 
other is maintained. Unfortunately, the fall of the one does 
not involve the maintenance of the other. Leibniz has acquired ~ 
much credit for the vaunted interconnection of his views in 
these two departments, and few seem to have perceived how 
false his boast really is. As a matter of fact, the want of s~r^--< 
connection is, I think, quite one of the weakest points in his 
system. » 

The problem of impact was one which pre-occupied the 
mathematicians of Leibniz's day far more than those of our own. 
It was solved only after he had acquired his mathematical 
equipment, and filled his mind to an extent which accounts for 
several curious features of his theory of matter. He appears to 
have quite unduly neglected impacts which are not perfectly 
elastic, and to have held (though he never definitely contends) 
that if bodies were only taken small enough, they could always 
be treated as perfectly elastic. Impact was ultimately, for him, i 
the only form of dynamical interaction. He definitely rejeclied, 
as ultimately valid, the Newtonian gravitation, holding, with 
mostjn:iodeni5,.Miat it jnust be _explained by all- ^ 

peryading_ fluid, (Perfect elasticity was ultimately required, if , 
his law of the conservation of Vis Viva was to be preserved, 
since, when the coeflficient of restitution is less than unity (as 
it always is in practice). Vis Viva is apparently lost.) His 
reply to this objection was that it is absorbed by the small 
parts of bodies — transformed, in modern phraseology, from 
molar into molecular motion (N. E. 669—670; G. M. yi. 
230 — 231). But if impact be the ultimate form of inter- 
action, this answer can only serve if the smaller parts which 
receive the motion are themselves perfectly elastic. When 
pressed by Huygens on this point, Leibniz meanly evades the 



90 THE PHILOSOPHY OF DYNAMICS. 

difficulty by denying that there are any last elements of bodies 
(G. M. II. 157). But a further difficulty remains, which is this. 
Impact is only elastic, according to Leibniz, because of a " subtle 
and penetrating fluid, whose motion is disturbed by the tension, 
or by the change of the elasticity. And as this fluid must 
be itself in turn composed of little solid bodies, elastic among 
themselves, we see that this replication of solids and fluids con- 
[ tinues to infinity " (N. E. p. 668 ; G. M. vi. 228). He proceeds 
j to confess that elasticity is necessary to the conservation of Vis 
1 Viva. Again he says — and this is an argument by which he 
often suggests the doctrine of monads : — " It is true that this 
conservation of force can only be obtained by putting elasticity 
everywhere in matter, and that a conclusion follows which will 
appear strange to those who do not sufficiently conceive the 
marvels of things: this is, that there are, so to speak, worlds 
in the smallest bodies, since every body, however small it may 
be, has elasticity, and consequently is surrounded and pene- 
trated by a fluid as subtle, in relation to it, as that which makes 
the elasticity of sensible bodies can be in relation to us ; and 
that therefore there are no first elements, since we must say as 
much of the smallest portion of the most subtle fluid that can 
[ be supposed " (G. III. 57). But it must be evident that, in the 
end, the motion of his fluid must be regulated by something 
other than the laws of elastic impact, since the elasticity of 
I what is comparatively solid is only due to the presence of what 
' is comparatively fluid. In order to develop the theory of an 
all-pervading fluid, Leibniz needed, what in his day did not 
exist, either Hydrodynamics or the modern Dynamics of the 
ether. 

44. There are, speaking broadly, three_, greats types ^ 

/ dynamical theory. There is the doctrine of hard extended 

atoms, for which the theory of impact is the appropriate 

I weapon. There is the doctrine of the plenum, of an aH-pervad- 

ing_fluid, for which the modern doctrine of the ether — the 

theory of Electricity, in fact — has at last partially forged the 

necessary weapons. And finally, there is the doctrine of unex- 

tended centres of force, with action a,t _ a distance^ for which 

Newton supplied the required Mathematics. <^ Leibniz failed to 

grasp these alternatives, and thus, from his love of a middle 



THE PHILOSOPHY OF DYNAMICS. 91 

position, fell between, not twOj bu_t three stools, y His view of 
impact as the fundamental phenomenon of Dynamics should 
have led him to the theory of extended atoms, supported by 
Gassendi, and, in his own day, by Huygens. His belief in the 
plenum and the fluid ether should have led him to the second 
theory, and to the investigation of fluid motion. His relational ; 
theory of space, and his whole doctrine of monads, should have 
led him, as it led Boscovich, Kant' and Lotze, to the theory of 
unextended centres of force. The failure to choose between 
these alternatives made his Dynamics a mass of confusions. 
The true Leibnizian Dynamics is not his own, but that of | 
Boscovich". This theory is a simple development of the ; 
Newtonian Dynamics, in which all matter consists of material ' 
points, and all action is action at a distance. These material j 
points are unextended like the monads, to which Boscovich 
appeals as analogous*; and in order to preserve their mutual 
independence, it is only necessary to regard the attraction or 
repulsion as due to the perception of one monad by the other, 
which, as a matter of fact, Leibniz actually does. Why, then, 
was this theory not that of Leibniz ? 

(There was, T think, to begin with, in later life, a personal 
reason.) Leibniz had quarrelled with Newton concerning the r 
Calculus, and he did not choose to -admit that Newton had 
anything to teach him*. He therefore rejected gravitation as 
an ultimate account of things, giving as his reason that action 
at a distance is impossible. But this personal reason can only i 
have operated after the publication of the Principia in 1687, 
by which date Leibniz had constructed both his philosophy and 
his Dynamics. It becomes necessary, therefore, to search for 
more objective reasons. 

' That Kant's theory of space in the Metaphysische Anfangsgriivde der 
Naturwissenschaft is different from that of the Kritik, has been often observed. 
See Vaihinger's Commentar, p. 224 ff. 

" Theoria Philosophiae Naturalis. See esp. Part I, § 138 ff. 

' Venetian edition of 1763, p. xxv. Boscovich differs from Newtonian 
Dynamics chiefly in assuming that, at very small distances, the force between 
two particles is repulsive. He differs from the Newtonian philosophy by regard- 
ing action at a distance as ultimate. 

" It has even been suggested — and the suggestion appears very probably 
correct — that Leibniz never took the trouble to read the Principia. See 
Guhrauer, op. cit. Vol. i. p. 297. 



92 THE PHILOSOPHY OF DYNAMICS. 

Leibniz rejected atoms, the vacuum, and action at a distance. 
His grounds for these three rejections must be now examined. 

45. (1) Against extended atoms he had, I think, fairly 
valid grounds. These are best set forth in his correspondence 
with Huygens, who maintained atoms. (See G. M. il. pp. 136, 
145, 155 — 7). In the first place, the extended atom is 
composed of parts, since extension is repetition ; it cannot, 
therefore, afford a metaphysical solution of the composition of 
matter. Moreover, if the laws of motion are to be preserved, 
the atom must be perfectly elastic,-which is impossible since it 
must also be perfectly hard, and can contain no " subtle fluid." 
Again there is a breach of the law of continuity in assuming 
infinite hardness and absolute indivisibility to emerge suddenly 
when a certain stage is reached in division. And primitive 
rigidity is, in any case, a quality wholly without reason, and 
therefore inadmissible. In short, infrangible atoms would be a 
perpetual miracle. These arguments have been urged many 
times since, and are, one may suppose, on the whole valid. 

46. (2) With regard to the vacuum, Leibniz relied mainly 
on the argument from what he called metaphysical perfection. 
He admitted that a vacuum is conceivable (N. E. 157 ; G. v. 
140), but held that, wherever there is ro6m, God might have 
placed matter without harm to anything else. Since, generally, 
the more existence the better, God would not have neglected 
the opportunity for creation, and therefore there is matter 
everywhere (D. 240, 253 ; G. vii. 356, 378). This principle of 
metaphysical perfection will be discussed later ; for the present 
I confine myself to less theological arguments. A very weak 
argument, which Leibniz sometimes permits himself, is, that 
there could be no sufficient reason for determining the propor- 
tion of vacuum to filled space, and therefore there can be no 
vacuum at all (D. 253 ; G. ii. 475 ; vii. 378). The only argu- 
ment which attempts to be precise is one which is fatally 
unsound. If space be an attribute, Leibniz says, of what can 
empty space be an attribute (D. 248 ; G. vii. 372) ? But space, 
for him, is a relation, not an attribute; his whole argument 
against the view that space is composed of points depends, as 
we shall see in Chapter IX., upon the fundamental relation of 
distance. He has, in fact, no valid arguments whatever against 



THE PHILOSOPHY OF DYNAMICS. 93 

a vacuum. He seems to regard a belief in it as necessarily 
associated with a belief in extended atoms — " atoms and the 
void " are always spoken of together. In fact, when action at a 
distance is rejected, the two are necessarily connected ; since 
unextended atoms must act at a distance, if there is to be any 
dynamical action at all^- 

47. (3) This brings me to Leibniz's grounds against I '^"'^ 
action at a distance. I cannot discover, on this point, anything j 
beyond vulgar prejudice. Both on this and on the previous f 
point, his immediate followers, under the influence of Newton, i 
abandoned the views of their master, which seem to have been 
mainly due to a lingering Cartesian prejudice. The spatial and i 
temporal contiguity of cause and efifect are apparently placed 

on a level. " A man will have an equal right to say that any- 
thing is the result of anything, if that which is absent in space or 
time can, without intermediary, operate here and now" (D. 115; 
G. IV. 507). With regard to time, though a difficulty arises 
from continuity, the maxim may be allowed ; but with regard 
to space, it is precluded, as a metaphysical axiom, by the denial 
of transeunt action. For since nothing really acts on anything 
else, there $eems no possible metaphysical reason why, in 
monads which mirror the whole universe, the perception of 
what is distant should not be a cause, just as much as the 
perception of what is near. There seems, therefore, in Leibniz's 
system, no metaphysical ground for the maxim ; and in his time 
(which was that of Newton), there was certainly no dynamical 
ground. The denial of action at a distance must, therefore, be [ 
classed as a mere prejudice, and one, moreover, which had a 
most pernicious effect upon the relation of Leibniz's Dynamics 
to his Metaphysics. 

48. I come now to another purpose which the doctrine of I 
force was designed to fulfil. It showed, in the first place, that I 

' On one minor point, however, namely the possibility of motion in a 
plenum, Leibniz is unquestionably in the right. Locke had maintained that 
there must be empty space, or else there would be no room for motion. Leibniz 
rightly rephes (N. E. pp. 53—4 ; L. 385 ; G. v. 52), that if matter be fluid, this 
difficulty is obviated. It should indeed be obvious, even to the non-mathematical, 
that motion in a closed circuit is possible for a fluid. It is a pity philosophers 
have allowed themselves to repeat this argument, which a, week's study of 
Hydrodynamics would suffice to dispel. The complete answer to it is contained 
in what is called the equation of continuity. 



94 THE PHILOSOPHY OF DYNAMICS. 

actual secondary matter — as opposed to primary matter, which 
is a mere abstraction — is essentially active, as everything 
substantial must be. But it also attempted to show — what is 
essential to the doctrine of monads — that every piece of matter 
has its own force, and is the source of all its own changes. It 
was necessary, as we saw in Chapter IV., to maintain the 
plurality of independent causal series, and thus to exhibit force 
as really affecting only the body in which it was, not those 
upon which it apparently acted. Here Leibniz, quite uncon- 
sciously, took one side of what appears to be an antinomy, and 
appealed to his Dynamics as proving the thesis only, when it 
proved, with quite equal evidence, the antithesis also\ This 
brings us to the aspect of force in which it confers indi- 
viduality* — an aspect which Leibniz also employs to prove the 
necessity of force. Without it, he says, all matter would be 
alike, and therefore motion, since space is a plenum, would 
make no difference (D. 122 ; G. iv. 512 — 3). This argument is 
certainly valid, on a relational theory of space, as against those 
(Cartesians or moderns) who hold to the relativity of motion, 
while they reduce all motion to vortices in a perfect fluid. But 
this is a digression, from which we must return to Dynamics 
and impact. 

I Every body, we are told, is really moved, not by other 
1 bodies, but by its own force. Thus in the successive impacts 
of a number of balls, " each ball repelled from the next one 
impinging on it, is set in motion by its mvn force, viz. its 
elasticity" (D. 124; G. iv. 515). The laws of motion, Leibniz 
thinks, compel us to admit independent causal action on the 
part of each particle of matter, and it is only by such action 
that we can free the idea of motion from a relativity which 
would make it wholly indeterminate. Therefore there must be, 
in each particle of matter, a force or activity from which its 
changes spring, by which we can give a meaning to a state of 
motion, and connect the states of a body at successive instants. 

> See §§ 49, 50. 

2 This is connected with the doctrine of activity as the essence of in- 
dividuality — a doctrine with which, by the way, Spinoza's dictum may be 
compared, that "desire is the very nature or essence of a person." Ethics, 
Pt. III. Prop. IX. Schol. and Prop. Lvn. 



THE PHILOSOPHY OF DYNAMICS. 95 

Force is related to materia prima as form to matter in the 
Aristotelian sense. " Because of form every body always acts, 
and because of matter every body always endures and resists " 
(N. E. 673; G. M. vi. 237). In active force is the entelechy, 
analogous to a soul, whose nature consists in a certain perpetual 
law of its series of changes, which it spontaneously carries out 
(G. II. 171). It is this force which constitutes the identity of 
each piece of matter, and differentiates it -from all other pieces. 
And Leibniz endeavours, as his metaphysics requires, to show 
that force only acts on the body in which it is, and never on 
any other body. Cases where a body appears to be acted upon 
by another are called cases of passion, but even here, the 
appearance is deceptive. " The passion of every body is spon- 
taneous, or arises from internal force, though upon occasion of 
something external. I understand here, however, passion proper, 
which arises from percussion, or which remains the same, what- 
ever hypothesis is finally assigned, or to whatever we finally 
ascribe absolute rest or motion. For since the percussion is the 
same, to whatever at length true motion belongs, it follows that 
the result of the percussion is distributed equally between both, 
and thus both act equally in the encounter, and thus half the 
result arises from the action of the one, the other half from the 
action of the other; and since half also of tlie result or passion 
is in one, half in the other, it is sufficient that we derive the 
passion which is in one from the action which is also in itself, 
and we need no influence of the one upon the other, although 
by the one an occasion is furnished to the action of the other, 
which is producing a change in itself" (N. E. 688; G. M. VI. 251). 
49. To bring this doctrine into harmony with the facts, a 
further distinction was required between primitive and deriva- 
tive force. The latter, which is a modification of the former, is 
the actual present state while tending to the future. The primi- 
tive force is persistent, and is, as it were, the law of the series, 
while the derived force is the determination designating a 
particular term of the series (G. ii. 262). "Active force," 

Leibniz says, " is twofold, n&melj primitive, which exists 

in every corporeal substance per se (since I think a wholly 
quiescent body abhorrent to the nature of things), or derivative, 
which by a limitation, as it were, of the primitive, resulting 



96 THE PHILOSOPHY OF DYNAMICS. 

through the conflicts of bodies with each other, is variously 
exercised. Aad, indeed, the primitive force (which is nothing 
other than the first entelechy) corresponds to the soul or 
substantial form, but for this very reason pertains only to 
general causes, which cannot suffice for the explanation of 
phenomena. And so we agree with those who deny that forms 
must be employed in deducing the particular and special 
causes of sensible things " (N. E. 672 ; G. M. vi. 236). The 
primitive force is constant in each body throughout all time ; 
the sum of derived forces throughout the universe is also 
constant, being what Leibniz calls Vis Viva, and what is still 
sometimes so called, which is double what is now known as 
kinetic energy (G. III. 4o7). "Derivative force is what some 
call impetus, that is a conatus or tendency to some determinate 
motion, by which the primitive force, or principle of action, is 
modified. This (the derivative force) I have shown to be not 
conserved the same in the same body, but yet being distributed 
among many bodies, to preserve a constant sum, and to diifer 
from motion, whose quantity is not conserved" (N. E. 702; 
G. IV. 396). 

In this argument, it must be evident that, so far from 

basing Metaphysics upon Dynamics, Leibniz has inferred, on 

purely metaphysical grounds, a primitive force of which no 

dynamical use is made'. What was useftil in Dynamics was, 

not the primitive force, which was constant in each separate 

piece of matter, but the derivative force, which was transferred 

I from body to body. The primitive force was thus invoked for 

j purely metaphysical reasons, and could not validly be used to 

1 show that Dynamics supported the doctrine of the inde- 

I pendence of substances. Here again, I think, as in the case 

of continuity, there is an antinomy which Leibniz refused to 

face. The total effect on any particle is, dynamically, made 

up of effects caused by all other particles ; thus the separate 

causation of separate elements seems conceded. But none of 

these sepai;ate effects ever happen : they are all mathematical 

1 Cf. G. II. 251 : " Every modification presupposes something durable. 
Therefore when you say, ' Let us suppose that nothing is to be found in bodies 
except derivative forces,' I reply that this is not a possible hypothesis." Of. also 
G. n. 270. 



THE PHILOSOPHY OF DYNAMICS. 9'7 

fictions. What really happens is the sum of effects, i.e. the 
effect of the sum or of the whole. Thus even when a thing 
is defined as one causal series, we can hardly escape the 
admission, which however is directly self-contradictory, that 
things do, after all, interact. 

And this is, in fact, admitted practically in Leibniz's 
writings. Although Dynamics requires us to assign causal 
action to each piece of matter, it requires us, just as much, 
to take account of all material particles in discussing what 
will happen to any one. That is, we require, on a purely 
dynamical basis, to admit transeunt action, the action of one 
thing on another. This was not avoided by Leibniz : on the 
contrary, the purely material world remained, for him, one in 
which every motion affects every other, though direct inter- 
action occurs only in impact. " All is a plenum (and thus 
all matter is connected together), and in the plenum every 
motion has an effect upon distant bodies in proportion to their 
distance, so that each body not only is affected by those which 
are in contact with it, and in some way feels the effect of 
everything that happens to them, but also is mediately affected 
by bodies touching those with which it is in immediate 
contact. Wherefore it follows that this intercommunication 
of things extends to any distance, however great. And conse- 
quently every body feels the effect of all that takes place in 
the universe " (Monadology, § 61 ; L. 251 ; D. 227 ; G. vi. 617). 
He then proceeds to deduce the proposition that all substances 
mirror the universe from this standpoint, which is diametrically 
opposite to that of the independence of all material particles'. 
He explained this apparent interaction by a subjective theory, 
in which motions became merely representations in all monads, 
because all monads mirror the universe. The true account 
of the matter became, that representations of causes are 
causes of representations of effects (G. iv. 533), a kind of 
Berkeleian theory, which renders it absurd to deduce the ac- 
tivity of substance from anything whatever in Dynamics. 

Moreover, if — as one must suppose — what seems to be 
motion is a real change in some assemblage of monads, and is 
therefore part of an independent causal series, its perception, 

1 Of. G. II. 112. 

B. L. 7 



98 THE PHILOSOPHY OF DYNAMICS. 

the subjective motion, is also part of such a series, and there 
are as many independent causal series in each monad as there 
are monads in the world which it mirrors. This difBculty, 
however, may be left till we come to the pre-established 
harmony. 

I 50. There remains one last and principal difficulty, a 
j difficulty which, so far as I know, no existing theory of Dy- 
i namics can avoid. When a particle is subject to several forces, 
they are compounded by the parallelogram law, and the re- 
sultant is regarded as their sum. It is held that each inde- 
pendently produces its effect, and that the resultant effect 
is the sum of the partial effects. Thus " every conation is 
compatible with every other, since every motion can be com- 
pounded with every other to give a third motion, which can 
always be determined geometrically. And thus it did not 
appear how a conation could be naturally destroyed or with- 
drawn from a body" {Archiv fur Oesch. d. Phil. i. 578). If 
we are to admit particular causes, each of which, independently 
of all others, produces its effect, we must regard the resultant 
motion as compounded of its components. If we do not admit 
such particular causes, every part of matter, and therefore all 
matter, is incapable of causal action, and Dynamics (unless the 
descriptive school is in the right) becomes impossible. But it 
has not been generally perceived that a sum of motions, or 
forces, or vectors generally, is a sum in a quite peculiar sense — 
its constituents are not parts of it. This is a peculiarity of all 
addition of vectors, or even of quantities having sign. Thus no 
one of the constituent causes ever really produces its effect : 
the only effect is one compounded, in this special sense, of the 
effects which would have resulted if the causes had acted inde- 
pendently. This is a fundamental difficulty concerning the 
nature of addition, and explaining, I think, how Leibniz came to 
be so confused as to the causation of particulars by particulars. 
So great is this confusion, that it is not unfairly expressed 
by Wundt in the words : " Every substance determines itself, 
but this self-determination is determined by another sub- 
stance " {Die physikalischen Axiome, p. 57). 

Thus the attempt to establish, on the basis of Dynamics, 
a plurality of independent causal series, must be pronounced 



THE PHILOSOPHY OP DYNAMICS. 99 

a complete failure. Not only was it faulty in detail, but it 
was also mistaken in principle, since the result aimed at — 
the reduction of the whole series of dynamical phenomena 
to subjective series of perceptions — should have made the 
whole dynamical world a single series in each percipient 
monad. The confusion was due — as we shall find to be the 
case with most of Leibniz's confusions — to a failure to grasp the 
consequences, drawn boldly (except as to the thing in itself) i 
by Kant, of the subjectivity of space. In the next two "j" 
chapters, we shall have to consider a better argument, an 
argument from the difficulties of the continuum to the un- •/ 
reality of space, and the consequent non-spatial nature of the ■ 
monads. 



7—2 



CHAPTER VIII. 

THE PHILOSOPHY OF MATTER (CONTINUED). 

(6) As explaining continuity and extension. 

51. We now reach at last the central point of Leibniz's 
philosophy, the doctrine of extension and continuity. The most 
distinctive feature of Leibniz's thought is its pre-occupation 
with the "labyrinth of the continuum." (To find a thread 
through this labyrinth was one main purpose of the doctrine of 
monads — a purpose which, in Leibniz's own opinion, that 
doctrine completely fulfilled. And the problem of continuity 
might very well be taken, as Mr Latta takes it (L. 21), as the 
starting-point for an exposition of Leibniz : " How can that 
which is continuous consist of indivisible elements " ? To 
answer this question was, I think, one of the two chief aims of 
Leibniz's doctrine of substance and of all that is best in his 
philosophy. That I did not begin with this question, was due 
to motives of logical priority ; /'for the abstract doctrines which 
we have hitherto considered, though perhaps invented largely 
with a view to this problem, are logically prior to it: they form 
an apparatus which must be mastered before Leibniz's treat- 
ment of the present question can be understood.) 

The present chapter may be regarded as a commentary on 
the first two paragraphs of the Monadology. " The Monad, of 
which we shall here speak," Leibniz says, "is nothing but a 
simple substance, which enters into compounds. By ' simple ' 
is meant ' without parts.' And there must be simple substances, 
since there are compounds ; for a compound is nothing but a 
collection or aggregate of simple things" (L. 217; D. 218; 



7 7 



THE ANALYSIS OF EXTENSION. 101 

G. VI. 607). Now in this statement, I should like to point out 
the following presuppositions : (1) that the meaning of substance 
is known, (2) that we have grounds for assuming the existence 
of something substantial but complex, (3) that everything 
substantial and complex must ultimately be composed of parts 
which are not complex, i.e. have no parts, but are themselves 
simple substances. Of these presuppositions, the meaning of 
substance has been already discussed. The assumption that 
matter exists has also been shown to be essential. It remains 
to enquire why matter is an aggregate of substances, and why 
it must consist of simple substances. 

52. Leibniz starts, in this discussion, from the fact that 
matter is extended, and that extension is nothing but re- 
petition (cf G. II. 261). In this assertion, extension must be 
carefully distinguished from space. Extension, like duration, 
is a property of an extended thing, a property which it carries 
with it from place to place. "A body can change space, but 
cannot leave its extension " (D. 263 ; G. VII. 398) ; everything 
has its own extension and duration, but not its own space and 
time (D. 265 ; G. vii. 399). What we are now concerned with, 
then, is extension, not space. As regards extension, Leibniz 
took up a more or less common-sense attitude; as regards space, 
he had a complicated and rather paradoxical theory, which can 
only be fully dealt with after the doctrine of extension has been 
developed. The gregt errpr, in Leibniz, was the idea that exten- 
sio n and duration are prior to space and time. His logical 
order, as opposed to the order of discovery, is as follows : First 
comes the notion of substance, secondly the existence of many 
substances, thirdly extension, resulting from their repetition, 
and fourthly space, depending on extension, but adding the 
further notion of order, and taking away the dependence upon 
actual substances.^ The order of proof or of discovery, however, 
is different from this. The existence of many substances is - 
inferred from the fact of extension, by the contention that ex- 
tension means repetition. That extension logically presupposes 
space, being in fact the property of occupying so much space, 
seems sufficiently evident. Leibniz, however, overlooked this 
fact. He began with extension, as was indeed natural to any 
one who regarded substance as logically prior to space. It is 



102 THE ANALYSIS OF EXTENSION. 

instructive to contrast the order of Kant's Critique, which 
begins with space and time, and only then advances to the 
categories, among which are substance and attribute. That this 
was not Leibniz's order, is the main objection to his philosophy 
of the continuum. He began, instead, with a common-sense 
theory of extension and duration, which he vainly endeavoured 
to patch up by a paradoxical theory of space and time. 

53. In my last chapter (p. 78), I stated that one of 
Leibniz's arguments against the view that the essence of 
matter is extension was derived from the nature of exten- 
sion itself This argument we must now examine. Extension, 
he says, in a dialogue directed against Malebranche, is not a 
concrete, but the abstract of what is extended. This, he con- 
tinues, is the essential difference between his theory of sub- 
stance and the Cartesian theory advocated by Malebranche 
(G. VI. 582 — 4). " Besides extension," he says in another place, 
" there must be a subject which is extended, i.e. a substapce to 
which it belongs to be repeated or continued. For extension 
signifies only a repetition or continual multiplication of that 
which is extended, a plurality, continuity and coexistence of 
parts; and hence extension is not sufficient to explain the 
nature of the extended or repeated substance itself, the notion 
of which is anterior to that of its repetition " (D. 44 ; G. iv. 
467). And not only must there be a plurality of substances, 
but also — I suppose in order that the plurality may constitute 
a repetition — there must be a repeated or extended quality. 
Thus in milk there is a diffusion of whiteness, in the 'diamond 
a diffusion of hardness (G. vi. 584). But the diffusion of 
such qualities is only apparent, and is not to be found in the 
smallest parts. Thus the only quality which is properly ex- 
tended is resistance, which is the essence of rrmteria prima 
(N. E. p. 700 ; G. iv. 394). Thus the essence of materia prima 
is not extension, but is extended, and indeed is the only quality 
which can, strictly, be called extended: for it is the only quality 
which is common to all created substances, and thus repeated 
everywhere. / Extension or primary matter, Leibniz says, is 
nothing but a certain repetition of things in so far as they are 
similar or indiscernible. But this supposes things which are 
repeated, and have, in addition to common qualities, others 



THE ANALYSIS OF EXTENSION. 103 

which are peculiar (D. 176; F. de C. 28—30). This theory- 
explains two important points. First, it shows why all monads 
have materia prima ; for it is in virtue of this common quality 
that a collection of monads is extended. Secondly, it con- 
nects the Identity of Indiscernibles with the abstract and 
phenomenal nature of extension. For extension is a repetition 
of things in so far as they are indiscernible ; and thus, since no 
two things are really indiscernible, extension involves abstrac- 
tioft from those qualities in which they differ. Thus a collection 
of monads is only extended when we leave out of account 
everything except the materia prima of each monad and the 
general property of activity, and consider merely the repetition 
of these qualities. 

54. But materia prima, as we saw in the last chapter, and 
as appears further from the fact that two pieces of materia 
prima are indiscernible, is a mere abstraction ; the substances 
whose repetition results in extension must have other properties 
besides this pure passivity, namely the activity essential to 
substance, and the differences required to make them many. 
Now wherever there is repetition, there must be many indivis- 
ible substances. " Where there are only beings by aggregation," | 
Leibniz says, " there are not even real beings. For every being 
by aggregation presupposes beings endowed with a true unity, j 
since it only derives its reality from that of those of which 
it is composed, so that it will have none at all if every com- 
ponent is again a being by aggregation." If we admit aggre- j 
gates, "we must either come to mathematical points,... or to 
the atoms of Epicurus,... or we must avow that there is no 
reality in bodies, or, finally, we must recognize in them some 
substances which have a true unity " (G. ii. 96). The special 
objections to mathematical points I shall consider in connection 
with the continuum. The objections to atoms — and these 
apply also against points — are, that they are indiscernible, and 
that, if they are purely material, they cannot have activity. 
The objection to not admitting the reality of bodies seems to 
be, as I have already pointed out, nothing better than common 
sense; but this led Leibniz to prefer, if he could logically do so, 
the theory of " true unities " to the mere unreality of bodies. 
At the same time, it is remarkable that, in his early statements 



i04 THE ANALYSIS OF EXTENSION. 

of the doctrine of monads, he hesitates to allow real unities to 
all bodies, and inclines to think that there may be inanimate 
bodies without any unities, and therefore without reality (G. ii. 
77 and 127)'. His argument may, then, be stated thus : 
Assuming that what appears to us as matter is something real, 
it is evident that it must be a plurality. Now a plurality is 
only real if its constituents are real, and nothing is ultimately 
real except substances and their states. But the plurality, in 
this case, since its constituents exist simultaneously, is not a 
mere plurality of states ; therefore it is a plurality of substances, 
and substances are necessarily indivisible. Hence what appears 
to us as matter must be a collection of indivisible substa,nces. 
What is not truly one being, is not truly a being ; if it were of 
the essence of a body to have no unity, it would be of its 
essence to be a mere phenomenon (G. ii. 97). These real 
unities are what Leibniz calls entelechies or forms. These terms, 
which he borrowed from Aristotle, denote, when accurately 
used, not the whole monad, but its activity, or that in it which 
is analogous to a soul, as opposed to its materia prima, which 
is passive, and is matter also in the Aristotelian sense, opposed 
to form (cf G. ii. 252). 

What is the nature of these " true unities " involved in the 
reality of what appears as matter? This nature in general I 
shall discuss in Chapter XI.; for the present, I am concerned 
with it only in so far as it is required to explain extension. We 
shall have in the next chapter to investigate the abstract 
doctrine as to the continuous and the discrete, as to space and 
extension, which underlies this present argument ; but it will 
be well to begin with the more concrete form of Leibniz's 
difficult doctrine of the continuum. 

55. Leibniz distinguishes three kinds of points. " Atoms 

of matjer," he says, "are contrary to reason only ato^ns of 

substance, i.e. unities which are real and absolutely destitute of 
parts, are sources of actions and the absolute first principles of 
the composition of things, and, as it were, the last elements 
of the analysis of substances. They might be called meta- 
physical points; they possess a certain vitality and a kind of 
perception, and mathematical poiuts are their points of view to 
' Contrast Stein, op. cit. p. 167 note. 



THE ANALYSIS OF EXTENSION. 105 

express the universe. But when corporeal substances are com- 
pressed, all their organs together form only a physical point to 
our sight. Thus physical points are only indivisible in appearance ; 
mathematical points are exact, but they are merely modalities ; 
only metaphysical points or those of substance (constituted by 
forms or souls) are exact and real, and without them there would 
be nothing real, for without true unities there would not be 
multiplicity " (D. 76 ; L. 310—1 ; G. iv. 482). The expression 
" metaphysical points " is not usual, and is only employed, 
apparently, to bring out the connection with infinite division. 
We may put the matter thus : Space consists of an assemblage 
of relations of distance; the terms of such relations, taken 
simply as terms, are mathematical points. They are thus mere 
modalities, being a mere aspect or quality of the actual terms, 
which are metaphysical points or monads. The physical point, 
on the contrary, is an infinitesimal extension, of the kind used 
in the Infinitesimal Calculus. This is not truly indivisible, 
since it is, after all, a small extension, and extension is essenti- 
ally repetition^ The argument, then, is briefly this : Matter as ' 
such is extended ; extension is essentially plurality ; therefore 
the elements of what is extended cannot themselves be ex-j 
tended. A simple substance cannot be extended, since alii 
extension is composite (G. iii. 363). Atoms of matter are 
contrary to reason, because they would have to be indivisibles 
whose essence is divisibility. Hence the constituents of matter 
are not material, if what is material must be extended. But 
the constituents cannot be mathematical points, since these 
are purely abstract, are not existents, and do not compose 
extension. The constituents of what appears as matter, there- 
fore, are unextended, and are not mathematical points. They 
must be substances, endowed with activity, and differing inter 
se because of the Identity of Indiscernibles. Hence there 
remains nothing, among the objects of experience, which these 
substances can be, except something analogous to souls. Souls 
are concrete existents, or substances, differing intei' se, and 
unextended. These, therefore, must be the constituents of what 
seem to be bodies. Bodies as such, i.e. as extended, are 
phenomena; but they are phenomena bene fundata, because 
they are the appearances of collections of real substances. The 



106 THE ANALYSIS OF EXTENSION. 

nature of these is force, and they are indivisible like our minds 
(D. 72 ; L. 301 ; G. iv. 479). 

The argument is excellently stated in a letter to De Voider 
(G. II. 267). De Voider says : Extension being necessary to a 
mathematical body, it is rightly concluded that, in such a body, 
no indivisible unities can be assigned. But this does not prove 
the mathematical body to be destitute of reality. To this 
argument Leibniz makes a very full reply. What can be 
divided into several, he says, is an aggregate of several ; an 
aggregate is one only for the mind, and has no reality but what 
is conferred by its constituents. Hence there are in things 
indivisible unities, because otherwise there will be in things no 
true unities, nor any reality not derived, which is absurd. For 
where there is no true unity, there is no true multitude. And 
where there is no reality not derived, there is no reality at all, 
for this must at length be derived from some subject. Again, 
he says, I conclude that in the mass of bodies indivisible 
unities, or prime constituents, can be found. Bodies are always 
divisible and always divided, but not so the elements which 
constitute them. The mathematical body is not real, because 
it has no such constituents ; it is something mental, and desig- 
nates a mere plurality of parts. As number is not substance 
without things numbered, so the mathematical body, or exten- 
sion, is not substance, without activity and passivity. But in 
real corporeal things, the parts are not indefinite (as in space, 
which is a mental thing), but actually assigned in a certain 
manner, as nature institutes actual divisions and subdivisions 
according to the varieties of motion; and these divisions 
proceed to infinity, but none the less result in certain primary 
constituents or real unities, only infinite in number. But to 
speak strictly, matter is not composed of constitutive unities, but 
results from them, for matter or extended mass is only a well- 
founded phenomenon, and all reality consists of unities. There- 
fore phenomena can always be divided into lesser phenomena, 
and there are no least phenomena. Substantial unities are not 
parts, but foundations, of phenomena. 

56. Many things in this argument presuppose Leibniz's 
general position as to continuity, a position which, with his 
theory of space, must be left to the next Chapter. To represent 



THE ANALYSIS OF EXTENSION. 107 

fairly, however, the drift of Leibniz's argument from extension 
to monads, it must be remembered that he believed himself, on 
a purely dynamical basis, to have shown matter to be the 
appearance of something substantial. For force, which he 
regarded as equivalent to activity, is required by the laws of 
motion, and is required in each piece of matter. That there 
must be entelechies dispersed everywhere throughout matter, 
follows from the fact that principles of motion are thus dis- 
persed (G. VII. 330). And from this point of view, we may give 
a slightly better meaning, than before appeared, to the doctrine 
of force. Force is more real than motion, or even matter. 
Motion is not a cause, but an effect of force, and is no more a 
real being than time. But force is a real being, though matter 
is only a well-founded phenomenon (G. II. 115 ; iii. 457). Thus 
though matter and motion are only appearances, they are 
appearances of something having activity, and therefore of 
something substantial. If we asisume, as Leibniz always does, 
that our perceptions of matter correspond to a real world out- 
side us, then that world, on dynamical grounds, must contain 
forces, and therefore substances. The only difficulty is, to recon- 
cile this view with the arbitrary and infinite divisibility of 
matter. This difficulty brings us to the doctrine of infinity and 
continuity. 



CHAPTER IX. 

THE LABYRINTH OF THE CONTINUUM. 

57. In the last chapter, we saw that matter is a phe- 
nomenon, resulting from aggregates of real unities or monads. 
Extension is repetition, and the extended is therefore plural. 
But if what appears as matter is a plurality, it must be an 
infinite plurality. For whatever is extended, can be divided 
ad infinitum. Mass, says Leibniz, is discrete, i.e. an actual 
multitude, but composed of an infinity of units (G. ii. 379). 
Here we have Leibniz's belief in the actual infinite. An actual 
infinite has been generally regarded as inadmissible, and Leib- 
niz, in admitting it, is face to face with the problem of the 
continuum. ! At this point, therefore, it is necessary to examine 
his views about infinity, continuity, infinite number, and infinite 
-division. These must be dealt with before we proceed any 
farther with the description of the true unities or monads, since 
Leibniz professes to deduce the existence and nature of monads 
largely from the need of explaining the continuum. " In this 
consideration " (i.e. of monads), he says, " there occurs no exten- 
sion or composition of the continuum, and all difiiculties about 
points vanish. And it is this that I meant to say somewhere 
in my TModicie, namely that the difficulties of the continuum 
should admonish us that things are to be conceived in quite a 
different manner" (G. ii. 451; cf G. vi. 29). Again he says 
(G. II. 262): "The monad alone is a substance, body is sub- 
stances, not a substance ; nor can the difiiculties of the compo- 
sition of the continuum, and others allied to these, be otherwise 
evaded " ; and " nothing but Geometry can furnish a thread for 
the labyrinth of the composition of the continuum, of maxima 



THE LABYRINTH OF THE CONTINUUM. 109 

and minima, and of the unassignable and the infinite, and no 
one will arrive at a truly solid metaphysic who has not passed 
through that labyrinth'." Now what are the difficulties of 
the continuum, and how are they evaded? I cannot hope to 
succeed in making the subject plain, both because it is nearly 
the most difficult subject in philosophy, and because Leibniz's 
treatment offers special difficulties to the commentator. 

58. Every one who has ever heard of Leibniz knows that 
he believed in the actual infinite. Few quotations from him ' 
are more familiar than the following (D. 65 ; G. I. 416) : " I am 
so much in favour of the actual infinite, that, instead of admit- 
ting that nature abhors it, as is commonly said, I hold that 
nature affects it everywhere, in order the better to mark the 
perfections of its author. So I believe that there is no part of 
matter which is not, I do not say divisible, but actually divided ; 
and consequently the least particle must be regarded as a world 
full of an infinity of different creatures." Such passages, I say, 
are well known, and are embodied in the coramon remark that 
Leibniz believed in the actual infinite, i.e. in what a Hegelian 
would call the false infinite. But this is by no means the 
whole truth on the matter. To begin with, Leibniz denied 
infinite number, and supported his denial by very solid argu- 
ments". In the second place, he was familiar with the distinc- 
tion, afterwards used by Hegel, between the true and false 
infinite. " The true infinite," he says, " exists, strictly speaking, 
only in the Absolute, which is anterior to all composition, and 
is not formed by the addition of parts' " ; an infinite aggregate 
is not truly a whole, and therefore not truly infinite (G. ii. 

• Cohen, Infinitesimalmethode, p. 64 ; G. M. vn. 326. 

2 Cf. G. Ml. 629 ; I. 338 ; ii. 304—5 ; v. 144 ; N. E. p. 161. 

' N. E. p. 162; G. v. 144. Cf. the following passage: "I believe with Mr 
Locke that, strictly speaking, it may be said that there is no space, no time and 
no number which is infinite, but that it is only true that however great may 
be a space, a, time, or a number, there is always another greater than it, ad 
infinitum ; and that thus the true infinite is not found in a whole made up of 
parts. It is none the less, however, found elsewhere ; namely, in the absolute, 
which is without parts, and which has infiueuce upon compound things because 
they result from limitation of the absolute. Hence the positive infinite being 
nothing else than the absolute, it may be said that there is in this sense a posi- 
tive idea of the infinite, and that it is anterior to that of the finite " (D. 97 ; 
N. E. 16 — 17 ; G. v. 17 ; Erdmann's edition, p. 133. G.'s text appears to be 
defective). 



110 THE LABYRINTH OF THE CONTINUUM. 

304—5; N. E. pp. 161—3; G. v. 143—5). And these state- 
ments are not made in forgetfulness of his advocacy of the 
actual infinite. On the contrary, he says in one passage: 
" Arguments against actual infinity assume, that if this be 
admitted, there will be an infinite number, and that all infini- 
ties will be equal. But it is to be observed that an infinite 
aggregate is neither one whole, or possessed of magnitude, 
nor is it consistent with number" (G. II. 304.). -The actual 
infinite is thus defended on the express ground that it does not 
lead to infinite number. We must agree, therefore, that 
Leibniz's views as to infinity are by no means so simple or so 
naive as is often supposed. To expound the theory from which 
the above remarks follow, is a difficult attempt; but this 
attempt I must now undertake. 

I have already had occasion to mention Hegel, and I think 
an analogy in other respects may serve to throw light on 
Leibniz's arguments. In the first place, he often seems to 
imply, as we have already seen in connection with extension, 
the essentially Hegelian view that abstraction is falsification. 
In the second place, his argument on the present question, and 
his whole deduction of Monadism from the difficulties of the 
continuum, seems to bear a close analogy to a dialectical argu- 
ment. That is, to put the matter crudely, a result is accepted 
as true because it can be inferred from premisses admittedly 
false, and inconsistent with each other' Those who admire 
these two elements in Hegel's philosophy will think Leibniz's 
argument the better for containing them. But in any case, a 
comprehension of the argument is, if I am right in my interpre- 
tation, greatly facilitated by this analogy to a method which 
has grown familiar. 

1 The argument is not strictly dialectical, but the following statement shows 
its weakness. The general premiss is : Since matter has parts, there are many 
reals. Now the parts of matter are extended, and owing to infinite divisibility, 
the parts of the extended are always extended. But since extension means re- 
petition, what is repeated is ultimately not extended. Hence the parts of 
matter are ultimately not extended. Therefore it is self-contradictory to suppose 
that matter has parts. Hence the many reals are not parts of matter. (The 
argument is stated almost exactly in this form in G. vii. 552.) 

It is evident that this argument, in obtaining many reals, assumes that these 
are parts of matter — a premiss which it is compelled to deny in order to show 
that the reals are not material. 



THE LABYRINTH OF THE CONTINUUM. Ill 

59. In spite of the law of contipuity, Leibniz's philosophy ( 
may be described as a complete denial of the continuous. 
Repetition is discrete, he says, where aggregate parts are dis- 
cerned, as in number : it is continuous where the parts are 
indeterminate, and can be assumed in an infinite number of 
ways (N. E. p. 700; G. iv. 394). That anything actual is con- 
tinuous in this sense, Leibniz denies ; for though what is actual 
may have q,n infinite number of parts, these parts are not inde- 
terminate or arbitrary, but perfectly definite (G. ii. 379). Only 
space and time are continuous in Leibniz's sense, and these are 
purely ideal. In actuals, he says, the simple is prior to the 
aggregate ; in ideals, the whole is prior to the part (G. Ii. 379). 
Again he says that the continuum is ideal, because it involves 
indeterminate parts, whereas in the actual everything is deter- 
minate. The labyrinth of the continuum, he continues — and 
this is one of his favourite remarks — comes from looking for 
actual parts in the order of possibles, and indeterminate parts 
in the aggregate of actuals (G. ii. 282. Cf. lb. 379 ; iv. 491). 
This means that points and instants are not actual parts of 
space and time, which are ideal'; and that nothing extended 
(since the extended is indeterminate) can be a true component 
of an aggregate of substances, which is actual. As regards space 
and time, and number also, the finite whole is logically prior to 
the parts into which it may be divided ; as regards substance, 
on the contrary, the aggregate is logically subsequent to the 
individual substances which compose if. 

What Leibniz means, seems to be this. There are two sorts 
of indivisibles, namely simple ideas, and single substances. In 
the former sense, the number one is indivisible : it is a simple 
idea, logically prior to the fractions whose sum is one. These 
fractions presuppose it, and its simplicity is not disproved by 
the fact that there are an infinite number of fractions of which 
it may be composed. It is truer, in fact, to regard fractions as 
formed by dividing unity, than to regard unity as formed by 
compounding fractions. Similarly one half, abstractly taken, is a 
mere ratio, not the sum of two quarters ; the latter is only true 

1 Contrast Cohen, op. cit. p. 63, G. M. v. 385: "A point is an infinitely 
small or evanescent line." This seems only to be meant mathematically. 

2 Cf. G. M. IV. 89 ft. 



112 THE LABYRINTH OF THE CONTINUUM. 

of numbered things (G. iv. 491). Thus many who have philo- 
sophized about the point and unity have become confused, 
through not distinguishing resolution into aotions and division 
into parts (G. III. 583). Similarly, Leibniz thinks, the abstract 
line is not compounded (G. iv. 491), for what is true about the 
line is only the relation of distance, which, quS, relation, is 
indivisible. Composition exists only in concretes, i.e. in the 
masses of which these abstract lines mark the relations. In 
substantial actual things, the whole is a result or assemblage of 
simple substances (lb.). It is the confusion of the ideal and 
the actual, Leibniz says again, which has embroiled everything, 
and produced the labyrinth of the continuum. 

60. At this point, it seems essential to consider Leibniz's 
theory of space. This theory is more or less involved in every- 
thing that can be said about his philosophy; I have already 
said something about it, and much more will follow. But here 
a few explicit remarks will illustrate the doctrine of the con- 
tinuum. 

The ideals in which, according to Leibniz, the whole is 
prior to the part, are numbers, space, and time. As regards 
numbers, it is evident that unity, and even the other integers, 
are prior to fractions. As regards space and time, a similar 
result is attained by the relational theory. In all these cases, 
Leibniz would have done better to say boldly, that, though 
numbers and distances may be greater or smaller, they have no 
parts. With regard to fractions, he does say this (G. iv. 491), 
and this is what he means to say in all such cases. Ideals, if 
they are numbers, are concepts applicable to possible aggre- 
gates, but are not themselves aggregates ; if they are distances, 
they are possible relations, and must be distinguished from an 
extension which extends from one end of the distance to the 
other. 

61. There are two great types of spatial theory, the one 
represented by Newton, the other by Leibniz. These two are 
brought face to face in the controversy with Clarke. Both 
result from emphasizing one or other of the following pair 
of ideas. If we take two points A and B, they have (1) a 
distance, which is simply a relation between the two, (2) an 
actual length, consisting of so much space, and stretching from 



THE LABYRINTH OF THE CONTINUUM. 113 

A to B. If we insist on the former as the essence of space, we 
get a relational theory ; the terms A and B, whose distance is 
spatial, must themselves be non-spatial, since they are not 
relations. If we insist on the latter, the actual intervening 
length, we find it divisible into an infinite number of points 
each like the end points A and B. This alternative gives the 
Newtonian theory of absolute space, consisting, not in an 
assemblage of possible relations, but in an infinite collection of 
actual points. The objection to Newton's theory is, that it is 
self-contradictory ; the objection to Leibniz's, that it is plainly 
inconsistent with the facts, and, in the end, just as self-contra- 
dictory as Newton's. A theory free from both these defects is 
much to be desired, as it will be something which philosophy 
has not hitherto known. I shall return to Leibniz's arguments 
in my next chapter. For the present, I only wish to point out 
the consequences of his relational theory — consequences also 
drawn by Lotze and others who have advocated this theory. 

Space is an assemblage of possible relations of distance. 
These become actual only when the points A, B are occu- 
pied by actual substances. Distances may be greater or less, 
but cannot be divided into parts, since they are relations. 
(This consequence is not drawn by Leibniz, indeed it is ex- 
pressly denied ; but he uses part more generally than I am 
using it. He says, what suffices for me, that in space and time 
there are no divisions but such as are made by the mind [G. Ii. 
278 — 9]). And the terms which are distant, since space is 
relational, cannot themselves be spatial or extended. The 
distance, moreover, should be analyzed into predicates of the 
distant terms A and B ; this Leibniz does by representing 
distance as part of the manner in which A and B mirror one 
another. And thus a mathematical point, the place of A, is 
merely that quality of A in virtue of which, at any moment, it 
mirrors other things as it does. This is why mathematical 
points are the points of view of the monads, and also why they 
are mere modalities, and not parts of space. This view of space 
also explains why the whole is not composed of its parts. For 
the parts of a distance are merely other smaller relations of 
distance, and are in no way presupposed by the larger distance, 
which is logically independent of them. The distinction is, in 

B. L. 8 



114 THE LABYRINTH OF THE CONTINUUM. 

fact, that between intensive and extensive quantities. Exten- 
sive quantities presuppose all the constituents whose sum they 
are ; intensive quantities, on the contrary, do not in any way 
presuppose the existence of smaller quantities of the same 
kind. Leibniz's position is, then, that spatial and temporal 
quantities are relations, and thei-efore intensive ; while exten- 
sion is an extensive quantity, and presupposes actual parts in 
that which is extended'. 

The distinction between the composition of what is actual, 
and the resolution of what is ideal, is thus of great importance. 
It explains what Leibniz means by saying that an instant is 
not a part of time (G. III. 591), nor a mathematical point a part 
of the spatial continuum (D. 64, 76 ; L. 311 ; G. i. 416 ; ii. 
279 ; IV. 482). The spatial continuum is the assemblage of all 
possible distances. Mathematical points are merely positions, 
ti.e. possible terms for the relations of distance. Thus they are 
not of the same order as the possible distances which make up 
the spatial continuum ; they are not parts of this continuum. 
Indeed a distance, being a relation, has properly no parts, and 
thus we have no reason to resolve it into indivisible parts. 
What is extended in space, on the contrary, is concrete ; we 
have not merely distances, but also terms between which the 
distances hold. An abstract space is not plural, but a body 
which occupies that space must be plural. For instead of bare 
possibility, we now have something actual in the positions 
which, otherwise, are "mere modalities." 

62. We may put the whole argument briefly thus. 
(1) Nothing is absolutely real but indivisible substances and 
their various states (G. ii. 119). This is the outcome of the 
abstract logical doctrine with which I began my account of 

1 Thus in reply to Clarke, Leibniz says: "As for the objection that space 
and time are quantities, or rather things endowed with quantity, and that 
situation and order are not so, I answer, that order also has its quantity ; there 
is in it that which goes before, and that which follows; there is distance or 
interval. Eelative things have their quantity, as well as absolute ones. For 
instance, ratios or proportions in mathematics have their quantity, and are 
measured by logarithms ; and yet they are relations. And therefore, though 
time and space consist in relations, yet they have their quantity" (D. 270; G. 
VII. 404). Leibniz's views on intensive quantity were, however, by no means 
clear. 



THE LABYRINTH OF THE CONTINUUM. 115 

Leibniz ; it is presupposed in the argument from extension to 
monads, and must not be regarded as a result of that argu- 
ment. (2) What appears to us as matter is real, though qud 
matter it is phenomenal. The reality of what appears as 
matter is, as we saw, a mere prejudice. (3) Matter, qud phe- 
nomenon, is an aggregate, in fact an aggregate of an infinite 
number of parts. (4) An aggregate can have no reality but 
what it derives from its constituents, since only substances are 
real, and substances are indivisible. (5) Hence, if the reality 
of what appears to be matter is to be saved, this must consist 
of an infinite plurality of indivisible substances. 

63. But infinite number is self-contradictory, and we 
cannot be content with the assertion that there is an infinite 
number of monads. To evade this argument, Leibniz makes a 
very bold use of his principle that, in concretes, the part is 
prior to the whole, and that nothing is absolutely real but 
indivisible substances and their various states. Being and 
unity, he says, are convertible terms (G. ii. 304). Aggregates, 
not having unity, are nothing but phenomena, for except the 
component monads, the rest (the unity of the aggregate, I 
suppose) is added by perception alone, by the very fact of their 
being perceived at one time (G. ii. 517). This remark is of the 
utmost importance. It is a legitimate outcome of Leibniz's 
general position, and is perhaps the best alternative which that 
position allowed him. At the same time, its implications, as 
will soon be evident, completely destroy the possibility of a 
plurality of substances. 

Leibniz's position is this : that the notion of a whole can 
only be applied to what is substantially indivisible. Whatever 
is real about an aggregate is only the reality of its constituents 
taken one at a time ; the unity of a collection is what Leibniz 
calls semi-mental (G. ii. 304), and therefore the collection is 
phenomenal although its constituents are all real. One is the 
only number that is applicable to what is real, since any other 
number implies parts, and aggregates, like relations, are not 
" real beings." This explains how infinite number can be 
denied, while the actual infinite is admitted. " There is 
no infinite number," Leibniz says, "or line or other infinite 
quantity, if they are taken as veritable wholes" (N. E. p. 161 ; 

8—2 



116 THE LABYRINTH OF THE CONTINUUM. 

? G. V. 144). One whole mtist be one substance, and to what 
', is not one whole, number cannot properly be applied. The 
world is only verbally a whole (G. II. 305), and even a finite 
aggregate of monads is not a whole per se. The unity is 
mental or semi-mental. In most passages, Leibniz only applies 
this doctrine against infinite aggregates, but it is evident that 
it must apply equally against all aggregates. This Leibniz 
seems to have known. Thus he says (N. E. p. 148 ; G. v. 132) : 
" Perhaps a dozen or a score are only relations, and are consti- 
tuted only by relation to the understanding. The units are 
separate, and the understanding gathers them together, how- 
ever dispersed they may be." The same view is expressed at 
the end of the same chapter (Book II. Chap, xii.), where he 
says : " This unity of the idea of aggregates is very true, but at 
bottom, it must be confessed, this unity of collections is only a 
respect (rapport) or a relation, whose foundation is in what is 
found in each single substance by itself. And so these beings 
by aggregation have no other complete unity but that which is 
mental; and consequently their entity also is in some way 
mental or phenomenal, like that of the rainbow" (N. E. 149; 
G. V. 133). 

Now this position is a legitimate deduction from the theory 
that all propositions are to be reduced to the subject-predicate 
form. The assertion of a plurality of substances is not of this 
form — it does not assign predicates to a substance. Accord- 
ingly, as in other instances of a similar kind, Leibniz takes 
refuge, like many later philosophers, in the mind — one might 
almost say, in the synthetic unity of apperception. The mind, 
and the mind only, synthesizes the diversity of monads ; each 
separate monad is real apart from the perception of it, but a 
collection, as such, acquires only a precarious and derived 
reality from simultaneous perception. Thus the truth in the 
judgment of plurality is reduced to a judgment as to the state 
of every monad which perceives the plurality. It is only in 
such perception that a plurality forms a whole, and thus per- 
ception is defined by Leibniz as the expression of a multitude 
in a unity (G. III. 69). 

64. This notion, that propositions derive their truth from 
being believed, is one which I shall criticize in dealing with 



THE LABYRINTH OF THE CONTINUUM. 117 

God's relation to the eternal truths. For the present, it is 
enough to place a dilemma before Leibniz. If the plurality 
lies only in the percipient, there cannot be many percipients, | 
and thus the whole doctrine of monads collapses. If the plu- ' 
rality lies not only in the percipient, then there is a proposition I 
not reducible to the subject-predicate form, the basis for the ■ 
use of substance has fallen through, and the assertion of infinite 
aggregates, with all its contradictions, becomes quite inevitable 
for Leibniz. The boasted solution of the difficulties of the con- 
tinuum is thus resolved into smoke, and we are left with all the i 
problems of matter unanswered^ 

We have now seen the use which Leibniz made of his prin- 
ciple that in actuals the part is prior to the whole. We have 
seen how this enabled him to say that there is an infinite 
multitude of things, while at the same time denying infinite 
number. The multitude of things, he says, passes every finite 
number, or rather every number (G. VI. 629). We could only 
demand that some number should be applicable, if this multi- 
tude were a whole ; and that it is a whole, he denies, though 
the assertion of a whole is involved even in calling it a multi- 
tude. It cannot be denied that this position is consistent with 
his principles, and is even a direct result of them. But the 
consistency is of that kind which shows a mistake in the 
principles. The dilemma in which Leibniz is placed, is a direct i 
result of the combination of three premisses, which, as I asserted J 
in Chapter I. (p. 4), are hopelessly inconsistent. These three 
premisses are (1) that all propositions have a subject and a 
predicate, (2) that perception gives knowledge of a world not 
myself or my predicates, (3) that the Ego is an ultimate logical 
subject. 

1 The general principle thataU aggregates are phenomenal must not be 
confounded with the principle, which Leibniz also held, that infinite aggregates 
have no number. This latter principle is perhaps one of the best ways of 
escaping from the antinomy of infinite number. 



118 



CHAPTER X. 

THE THEORT OF SPACE AND TIME AND ITS RELATION TO 
MONADISM. 

' 65. I STATED broadly, in the preceding chapter, the nature 
of Leibniz's theory of space and time ; I wish to examine, in 
this chapter, what were its grounds, how far those grounds are 
the same as the grounds for monadism in general, and what 

■ was the relation of Leibniz's monads to space. (Much of what I 
shall say will be applicable also to Lotze', and generally to all 
theories which advocate a plurality of things. Let us begin 
with the theory of space. ) 

" I have several demonstrations," Leibniz says, " to confute 
the fancy of those who take space to be a substance, or at least 
an absolute being" (D. 243; G. vii. 363). These demonstra- 
tions, as they occur in Leibniz, proceed on the basis of the 

' traditional logic, and have, on that basis, very great force. For 
the traditional logic — the logic underlying all use of substance 
or of the Absolute — assumes, as I have endeavoured to show, 

' that all propositions have a subject and a predicate. If, now, 
space be admitted to exist per se, while the doctrine of substance 
is retained, there will be a relation between substances and the 
spaces they occupy. But this relation will be sui generis; it 
will not be a relation of subject and predicate, since each term 
of the relation exists, and may continue to exist though the 
relation be changed. Neither the thing nor the part of space 
is annihilated when the part is evacuated by the thing and 
reoccupied by a different thing. The relation, then, between a 

1 Although Lotze did not ultimately advocate plurality, but merged all 
in his M. 



THE THEORY OF SPACE AND TIME. 



119 



place and the substance occupying it, is one for which the 
traditional logic had no room. Accordingly, the independent 
existence of places was denied by careful philosophers, and 
admitted by Newton only because he was blind to its conse- 
quences. Clarke, to evade the consequences, made space and 
time parts of God's essence, a position which Leibniz easily 
showed to be absurd (D. 263; G. vii. 398). The contention 
Leibniz was really combating was, that space exists «er se, and 
not as a mere attribute of anything. 

We thus see why, for a philosophy of substance, it is 
essential to disprove the reality of space. A monist must 
contend that space is an attribute; a monadist, that space is 
an assemblage of relations. Against the former view, Leibniz 
is fairly strong ; in favour of the latter, he is inconclusive. But 
let us proceed to his arguments. 

" If there were no creatures," Leibniz says, " space and time 
would be only in the ideas of God " (D. 252 ; G. VII. 376—7). 
Against this view, Kant says : " We can never imagine that 
there should be no space, though we can quite well think that 
there should be no objects in it" (ed. Hartenstein, 1867, Vol. iii. 
p. 59). Here we have a sharp and definite opposition: Kant 
has drawn the consequence which Leibniz's theory is designed 
to avoids "If space be an absolute reality," Leibniz says, "far 
from being a property or an accident opposed to substance, it 
will be more subsistent than substances " (D. 248 ; G. vii. 373). 
What, then, were the arguments by which Leibniz disproved 
the reality of space ? 

66. The abstract logical argument, that space must, if ; 
real, be either subject or predicate, but is evidently neither, is 
not, so far as I know, set forth explicitly in Leibniz, though in 
the controversy with Clarke he urges that space, since it has 
parts, cannot be an attribute of God, and that empty space 
cannot be an attribute of anything (D. 264, 248 ; G. vii. 399, 
372). Against regarding space as an attribute, the real argu- ' 
ment is, that the essence of matter is not extension — an 
argument we have already seen to be conclusive. Against 
regarding space as a substance, or independent existent, 
Leibniz's favourite argument is derived from the Identity of 

' The Kantian subjectivity of space may be here left out of account. 



■t^l P 



120 THE THEORY OF SPACE AND TIME. 

' Indiscernibles and the Law of Sufficient Reason ; and this 
i argument applies equally against time. Space is absolutely 
uniform, and one point of it is just like another. Thus not 
only are the points indiscernible, but various arrangements of 
things would be indiscernible — for example, the actual arrange- 
ment and that which would result from turning the whole 
universe through any angle (D. 243 — 4 ; G. VII. 364). Again, 
if time were real, the world might have been created sooner, and 
no sufficient reason could appear for creating it at one time 
rather than another (D. 249 ; G. vii. 373). And generally, the 
universe as a whole cannot have different absolute positions in 
space or time, since these positions would be indiscernible, and 
therefore one and the same (D. 247 ; G. vii. 372). Besides 
these arguments, there are the contradictions of the continuum, 
I which we examined in the last chapter. Space and time, if 
i they are real, cannot be composed otherwise than of mathe- 
matical points ; but of these they can never be composed, since 
these are mere extremities ; two of them are not bigger than 
one, any more than two perfect darknesses are darker than one 
(G. II. 347). And as regards time, nothing of it exists but 
instants, and they are not properly parts of it, and how can a 
thing exist, whereof no part does ever exist (D. 268 ; G. vii. 402)? 
' 67. But if space and time are not real, what are they,? 
The answer is suggested by the argument from the Identity of 
Indiscernibles. From that argument it follows that there is no 
absolute position, but only mutual relations of things, from 
j which position is abstracted. Space is an order according to 
1 which situations are disposed, and abstract space is that order 
1 of situations, when they are conceived as being possible 
'^ : (D. 281 ; G. vii. 415). Time, again, is a being of reason 
exactly as much as space, bjjt co- pre- and post-existe nce are 
, something jeal (G. ii. 183). iBut if space is an order of 
situations, what are the situations themselves ? How are they 
to be explained relationally ?y' 

On this question, Leibniz is very explicit (D. 265 — 7 ; 
G. VII. 400 — 402). When the relation of situation of a body A 
to other bodies C, D, E etc., changes, while the mutual relations 
of situation of 0, D, E etc., do not change, we infer that the 
cause of change is in A, and not in 0, D, E etc. If now 



THE THEORY OF SPACE AND TIME. 121 

another body B has, to C, D, E etc., a precisely similar 
relation of situation to that which A formerly had, we say 
that B is in the same place as A was. But really there 
is nothing individually the same in the two cases ; for in 
the first case, the relations of situation were affections of A, 
while now they are affections of B, and the same individual 
accident cannot be in two different subjects. Thus the identity 
implied in speaking of the same place is an illusion ; there are 
only precisely similar relations of situation. Leibniz's account i 
is rendered unnecessarily self-contradictory by the introduction I 
of absolute motion, which, as we saw, he deduced from force i 
(cf. D. 269 ; G. vii. 404). From absolute motion he ought, like \ 
Newton, to have inferred absolute position. But his account of ' 
situation can be freed from this inconsistency. He is anxious 
to give an unambiguous meaning to same place, so as to be 
able to say definitely that the two bodies A and B either are, 
or are not, successively in the same place. But this, on his 
theory, is neither necessary nor possible. He must always 
specify the bodies by relation to which place is to be estimated, 
and must admit, as he may without contradiction, that other 
bodies of reference would, equally legitimately, bring out a 
different result. His reference to the cause of change of ' 
situation is due to an inconsistency, fundamental in his 
Dynamics, and in all Dynamics which works with relative 
position, but avoidable, in a relational theory of space, so long 
as no reference to Dynamics is introduced. Thus we may 
accept the following definition : " Place is that which is the 
same in different moments to different existent things, when 

their relations of coexistence to certain other existents 

agree entirely together." But when he adds that these other 
existents "are supposed to continue fixed from one of these 
moments to the other," he is making a supposition which, on a 
relational theory, is wholly and absolutely devoid of meaning 
(D. 266; G. vii. 400). It is such additions which show the 
weakness of the theory. There is plainly something more than | 
relations about space, and those who try to deny this are 
unable, owing to obvious facts, to avoid contradicting them- 
selves. But by practice in denying the obvious, it must be 
admitted, the relational theory may acquire a high degree of 
internal self-consistency. 



122 THE THEORY OF SPACE AND TIME. 

68. I come now to another closely allied topic, namely, the 
relation of space to the monads. Space, we have seen, is some- 
thing purely ideal; it is a collection of abstract possible 
relations. Now relations must always be reduced to attributes 
of the related terms. To effect this reduction of spatial relations, 
the monads and their perceptions must be introduced. And 
here Leibniz ought to have found a great difficulty — a difficulty 
which besets every monadism, and generally every philosophy 
which, while admitting an external world, maintains the sub- 
jectivity of space. 

The difficulty is this. Spatial relations do not hold between 
monads, but only between simultaneous objects of perception 
of each monad'. Thus space is properly subjective, as in Kant. 
Nevertheless, the perceptions of different monads differ, owing 
to the difference of the points of view ; but points of view are 
mathematical points, and the assemblage of possible points of 
view is the assemblage of possible positions^. (Thus Leibniz 
had two theories of space, the first subjective and Kantian, the 
second giving an objective counterpart, i.e. the various points 
of view of the monads.) The difficulty is, that the objective 
counterpart cannot consist merely in the difference of points of 
view, unless the subjective space is purely subjective ; but if it 
be purely subjective, the ground for different points of view has 
disappeared, since there is no reason to believe that phenomena 
are bene fundata. 

The nature of this difficulty will be made clearer by ex- 
amining the development of Leibniz's views on the relation of 
the Monads to space. (We shall see that, when he was young, 
in accordance with his materialistic bias, he definitely regarded 
souls as occupying points in space, while later, after he had 
become persuaded of the unreality of space, he endeavoured 
more and more to emphasize the subjectivity of space at the 
expense of the objective counterpart.) 

69. "Many years ago," Leibniz wrote in 1709, "when my 
philosophy was not yet sufficiently mature, I located souls in 

y) points" (G. II. 372). From this early view he seems to have 

1 G. II. 444, 450—1, 378 ; m. 357, 623. 

" Of. G. n. 253, 324, 339, 438; iv. 439, 482—3 (D. 76; L. 311), 484—5 (D. 78; 
L. 314); vii. 303—4 (D. 102; L. 340—2). 



THE THEORY OF SPACE AND TIME. 123 

derived many of the premisses of his doctrine, and these pre- j 
misses he thereafter accepted as an established basis for further I 
argument. Forgetting that these premisses were themselves I 
derived from the reality of space, he was not afraid of using 
them to disprove that reality. Such, at least, appears to me a 
plausible view of his development. He would seem to have 
come very near to his theory of monads in 1671-2, and then, 
by his contact with Cartesianism, to have been led away, for a 
while, from his individualistic tendencies, returning to them 
only when he had proved the inadequacy of Cartesian 
Dynamics, and the falsity of the dictum that extension is the 
essence of matter. 

He had, before his journey to Paris, already come very near 
to the doctrine of monads. " I can prove," he says, " from the 
nature of motion... that mind acts on itself... that mind consists 
in a point or centre, and is therefore indivisible, incorruptible, 
immortal.... Mind is a little world, comprised in a point, and 
consisting of its ideas, as a centre, though indivisible, consists 
of angles" (G. I. 61). And in 1671 he says that his proofs 
of God and immortality rest on the difficult doctrine of the 
point, the instant, the indivisible, and conation — precisely the 
same difficulties as his later theory was designed to solve. 
" Mind itself," he continues, " consists properly in a single point 
of space, whereas a body occupies a place." "If we give the 
mind a larger place than a point, it is already a body, and has 
partes extra partes; it is not therefore immediately present to 
itself" But if we posit that the mind consists in a point, it is 
indivisible and indestructible. The body, he says, has a kernel 
of substance which is always preserved, and this kernel consists 
in a physical point, while the soul consists in a mathematical 
point (G. I. 52—4). 

70. In these early views there is a frank acceptance of the 
reality of space, and a materialism which reminds one of Karl 
Pearson's central telephone exchanged The mind, he says, 
must be in the place of concourse of all motions which are 
impressed by objects of sense (G. i. 53). It must have been 
soon apparent to Leibniz that this doctrine did not solve the 

' Grammar of Science, Chap. n. § 3. 



124 THE THEORY OF SPACE AND TIME. 

difficulties of the point and the instant, or afford a consistent 
theory of substance. And so we find, in his early published 
accounts of the doctrine of monads, a third kind of point added 
to the above two, namely the metaphysical point, while the 
mathematical point is no longer that in which the soul consists, 
but only its point of view (D. 76 ; L. 311 ; G. iv. 482—3). 

71. But even here space and the mathematical point 
retained more reality than was to be wished, and accordingly 
both the expression "metaphysical points," and the assertion 
that mathematical points are the points of view of substances, 
disappear after 16951 After this time, he still speaks of 
points of view, and always explains them on the analogy of 
spatial points from which the world is, as it were, seen in 
perspective (G. ii. 438 ; iii. 357). But he insists that this is 
07ily an analogy, without, however, telling us to what it is 
analogous. He seems to have been aware of the difficulty, for 
in his later writings he avoids any distinct statement as to the 
soul's uheity. Souls may have, he thinks, at least in relation 
to bodies, what may be called definitive ubeity, i.e. they are in 
a certain volume, without our being able to assign them any 
special point in that volume CN. E. 230 — 1 ; G. v. 205—6). In 
the last year of his life, he is even more negative in his 
remarks. " God," he says, " is not present to things by situa- 
tion, but by essence ; his presence is manifested by his imme- 
diate operation. The presence of the soul is of quite another 
nature. To say that it is diffused all over the body is to make 
it extended and divisible. To say it is, the whole of it, in every 
part of some body, is to make it divisible from itself. To fix it 
to a point, to diffuse it all over many points, are only abusive 
j expressions, idola tribus " (D. 245 — 6 ; G. vii. 365 — 6). After 
this purely negative statement, Leibniz advances to another 
topic. He seems, in fact, to have nothing better to say, than 
that there are three kinds of ubeity, circumscriptive, definitive, 
and repletive^ that the first belongs to bodies, the second to 

1 The disappearacce of the former is not to be asoribed solely to the discovery 
of the term monad in 1696, for he retained other terms — enteleohies, simple 
substances, forms etc. — in spite of the adoption of the word monad. 

' An opinion which, it is true, is quoted as that of the schools, but without 
disapproval. 



THE THEORY OF SPACE AND TIME. 125 

souls, and the third to God (N. E. 230 ; G. v. 205). The most 
definite statement is one in a letter to Lady Masham (G. iii. 
357) : " The question whether (a simple substance) is somewhere 
or nowhere, is one of words : for its nature does not consist in 
extension, but it is related to the extension which it represents; 
and so one must place the soul in the body, where is its point 
of view according to which it now represents the universe. To 
want anything more, and to enclose souls in dimensions, is to 
wish to imagine souls like bodies." Here, and in all other 
passages known to me, Leibniz refuses to face the fact that all 
monads represent the same world, and that this world is always 
imagined by him to have something analogous to the space of ; 
our perceptions. (He seems once, indeed, to have perceived ! 
that the argument from extension to plurality of substances in- 
volved an objective space, and to have accordingly repudiated 
this argument.) " What belongs to extension," he says, " must not 
be assigned to souls, nor must we derive their unity or plurality 
from the predicament of quantity, but from the predicament of 
substance, i.e. not from points, but from the primitive force of 
operation" (G. II. 372). This suggests that the argument from 
Dynamics is more fundamental than that from extension — a 
view which, as we have seen, cannot be maintained. A closer i 
investigation shows more and more hopeless confusions. (He ; 
tries to give position to monads by relation to bodies. Monads, 
he says, though they are not extended, have a certain kind of 
situation, i.e. an ordered relation of coexistence to other things, 
through the machine which they dominate. ) " Extended things 
involve many things having situation; but simple things, 
though they have not extension, yet must have situation in 
extension, though this cannot be designated punctatim as in 
incomplete phenomena" (G. ii. 253). Again he says that a 
simple substance, though it has no extension, has position, 
which is the foundation of extension, since extension is a 
simultaneous continuous repetition of position (G. ii. 339). As 
he also insists that an infinite number of points do not 
together make an extension (ib. 370), we must suppose the 
position, in this case also, to be presence in a volume, not in a 
point. This view, curiously enough, is definitely put forward in 
the New System, the same work in which he speaks of mathe- 



126 THE THEORY OF SPACE AND TIME. 

matical points as the points of view of souls. After explaining 
the union of soul and body by means of the pre-established 
harmony, he continues : " And we can hence understand how 
the soul has its seat ia the body by an immediate presence, 
which could not be greater, since the soul is in the body as the 
unit (or unity : the French is unit^ is in the resultant of units, 
which is the multitude\" This preposterous notion of imme- 
diate presence in a volume was rendered plausible by reference 
to the organic body or machine ; but as this in turn consisted 
of monads, a new explanation would have been required for 
their position. Souls, Leibniz says, are not to be considered as 
in points, but we may say they are in a place by correspond- 
ence, and thus are in the whole body which they animate (G. ii. 
371). But as the body in turn consists of monads, the obvious 
f' \ question arises : Where is the body ? None of his devices, in 

: short, give Leibniz any escape from an objec^ve spage, prior to 
the phenomenal and subjective space in each monad's per- 

1 ceptions ; and this ought to have been obvious to him, from 
-^^j the fact that there are not as many spaces as monads, but one 
space, and even one only for all possible worlds^. The conge- 
ries of relations and places which constitutes space is not only 
in the perceptions of the monads, but must be actually some- 

' thing which is perceived in all those perceptions. The confu- 
sions into which Leibniz falls are the penalty for taking exten- 

1 sion as prior to space, and they reveal a fundamental objection 

i to all monadisms. (For these, since they work with substance, 
must deny the reality of space; but to obtain a plurality of 
coexistent substances, they must surreptitiously assume that 
reality.) Spinoza, we may say, had shown that the actual world 
could not be explained by means of one substance; Leibniz 
showed that it could not be explained by means of many sub- 

I stances. It became necessary, therefore, to base metaphysics 
on some notion other than that of substance —a^task_not_yet 
, accomplished. 

1 G. IV. 485 ; D. 78 ; L. 314. Cf. Mr Latta's note on this passage. On the 
notion of presence by operation which Leibniz seems here to be thinking of, I 
shall speak later, when I come to the theory of soul and body. Leibniz, 
however, rejected with ridicule the view, which seems to follow from this theory, 
that souls are extended. See D. 267 ; G. vii. 402. 

2 Cf. D. 102 ; L. 340—2 ; G. vii. 308—4 ; ii. 379. 



THE THEORY OF SPACE AND TIME. 127 

72. (It remains to say something concerning time and 
chajQge. Here we have much fewer passages to refer to, and — 
so far as I know — no_thOTOugh discussion _after Leibniz's 
philoso phy i s matare.) Time, like space, is relational and 
subjective (cf D. 244; G. vil. 364; ii. 183). Its subjectivity 
has been already discussed in Chapter IV.; I wish here to 
discuss only its relativity. Leibniz does not seem to have 
perceived clearly what is involved in this. What is involved is, 
that in time, as in space, we have only distances, not lengths or 
points. That is, we have only iefore and after : events are not 
at a certain time, but those which are not simultaneous have a 
distance, expressed by saying that one is before the Other. 
This distance does not consist of points of time, so that we 
cannot say time has elapsed between two events. Other events 
may be between them — i.e. there may be events before one of 
our pair and after the other. But when two events have no 
event between them, they have merely a relation of before and 
after, without being separated by a series of moments. No 
event can last for any length of time, for there is no such thing 
as a length of time — there are only different events forming a 
series. Nor can we say that events last for an instant, since 
there are no instants. Thus there will be no such thing as a 
state of change, for this implies continuity. In motion, for 
example, we shall have different spatial positions occupied 
serially, but there will not be a passage from one to the other. 
It is true, Leibniz holds time to be a plenum (D. 281 ; G. VII. 
415) — a phrase which, as in space, can only mean, on a re- 
lational theory, that the smallest distances which actually 
occur are infinitesimal. Or rather, since, as Leibniz confesses 
(N. E. 159 ; G. v. 142), if two events were only separated by 
empty time, we could never discover the amount of such time, 
we must mean, when we say that time is a plenum, that 
between any two given events there is always another. But 
this view leaves the difficulties of continuity intact. 

When applied to motion, this view must not be expressed 
as saying that a body passes instantaneously from one place to 
another, and then remains there till it takes another leap. For 
this would imply that time elapsed between successive leaps, 
whereas the essence of the relational view is, that no time 



128 THE THEORY OF SPACE AND TIME. 

elapses : presence in one position in space is separated by a 
temporal distance, but not by a temporal length (v. p. 112), from 
presence at the position next occupied. Nor must we say, that 
a moving body is sometimes in motion and sometimes at rest ; 
in fact it can never, in the usual acceptation of the words, be 
either at rest or in motion. To say that a body is at rest, can 
only mean that its occupancy of a certain position in space is 
simultaneous (simultaneity being an ultimate relation) with 
two events which are not simultaneous with each other. And 
to say that a body is in motion will mean that its occupancy 
of one position and its occupancy of another are successive. 
But from this we shall never arrive at a state of a motion, even 
by taking an infinite number of spatial positions successively 
occupied. Exactly the same argument will apply to change in 
general, and a state of motion or change, as we have seen, is 
absolutely necessary to Leibniz's doctrine of activity '. 

! 73. The relational theory of time is altogether more 
paradoxical than that of space, and is rendered so by the fact 
that the past and future do not exist in the same sense as the 

i present. (^Moreover Leibniz admits that previous time has a 
priority of nature over subsequent time (G. III. 582), and that 
there was probably a first event, i.e. the creation (D. 274 ; 
G. VII. 408) — admissions which greatly add to the difficulty of 
maintaining the relativity of temporal position.) There is, 
moreover, in all monadisms, an asymmetry in regard to the 
relation of things to space and time, for which there is, so far 
as I know, nothing to urge except the apparent persistence of 
the Ego. It is held. that substances persist through time, but 
do not pervade space. Difference of spatial position at the 
same time shows difference of substance, but difference of 
temporal position at the same place does not show this. The 
time-order consists of relations between predicates, the space- 
order holds between substances. For this important assumption 
there is, in Leibniz, no sort of argument. It is made con- 
fusedly by common sense as regards things, and seems to be 
borrowed thence quite uncritically by all monadisms. That it 

1 Cf. Or. IV. 513. I know of no discussion of the difficulties of motion except 
that in the Archiv f. Gesch. der Phil. i. 213 — i which belongs to 1676, and 
throws little light upon what Leibniz thought when his philosophy was mature. 



THE THEORY OF SPACE AND TIME. ]29 

should have been so little discussed, even by those who believed 
that they were treating time and space quite similarly, is a 
curious and unfortunate instance of the strength of psychological 
imagination. 

74. It would thus appear that Leibniz, more or less uncon- 1 
sciously, had two theories of space and time, the one subjective, 1 
giving merely relations among the perceptions of each monad, , 
the other objective, giving to the relations among perceptions 
that counterpart, in the objects of perception, which is one and 
the same for all monads and even for all possible worlds. This i 
counterpart Leibniz would fain have regarded as a "purely 
ideal thing," a " being of reason," a " mental entity." I wish to i 
repeat briefly the reasons which make these abusive epithets 
applicable only to subjective space and time, not to that counter- 
part which they must have outside' perception. This will be 
effected by recapitulating the arguments on which the Monado- 
logy is based. 

"Body is an aggregate of substances," Leibniz says, "and 
not properly one substance. It must be, consequently, that 
everywhere in body there are found indivisible substances" 
(D. 38 ; G. II. 135'). This argument would vanish if space i 
were purely subjective, and extended body, as with Kant, a pure 
phenomenon. Another favourite argument for difference among i 
monads, which, according to Leibniz, is on a level with geo- 
metrical proofs (G. II. 295), is, that if they were not different, 
motion in a plenum would make no difference, for each place 
could receive only the equivalent of what it had before (D. 219; 
L. 221 ; G. VI. 608) — again an argument involving a place 
which is not merely in the perceptions of monads. And this is 
to be connected with his argument, that thei-e must be ente- 
lechies dispersed throughout matter, since principles of motion 
are thus dispersed (G. Vll. 330). Another reason for the 
objectivity of space and time is, that they are orders of the 
possible as well as the actual, while yet, in some sense, they 
existed after the creation in a way different from that in which 
they had previously existed in the mind of God. In the origin 

• Of. G. n. 301 : " Since monads or principles of substantial unity are 
everywhere in matter, it follows hence that there must be an actual infinity, 
since there is no part, or part of a part, which does not contain monads." 

R. L. -9 



130 THE THEORY OF SPACE AND TIME. 

of things, we are told, a certain divine mathematics was 
employed to determine the greatest quantity of existence, 
" regard being had to the capacity of the time and of the place 
(or of the possible order of existence) " (D. 102 ; L. 341 ; G. vii. 
304). Now this possible order, before creation, existed only in 
the mind of God (D. 252 ; G. vii. 377), but after the creation, 
it existed in some other way ; (|or Leibniz definitely declares 
that space does not, like God, exist necessarily (G. vi. 405), 
though space as the mere object of God's understanding must, 

j of course, necessarily existpi Hence we must distinguish (1) 
space and time in the mind of God, (2) space and time in the 
perceptions of each monad, (3) objective space and time, which 

i existed after the creation, but not before. This third kind 
would, of course, for Leibniz, be still relational. Thus, he says 
(D. 209 ; L. 408 ; G. vi. 598), "There are simple substances 
everywhere, which are actually separated from each other by 
actions of their own, which continually change their rela- 
tions." But the important point is, that the relations, being 
between monads, not between the various perceptions of one 
monad, would be irreducible relations, not pairs of adjectives 
of monads. In the case of simultaneity, this is peculiarly 
obvious, and seems, indeed, to be presupposed in the idea of 
perception. If this be the fact, to deduce simultaneity from 
perception is a fatally vicious circle. 



131 



CHAPTER XI. 



THE NATURE OF MONADS IN GENERAL. 

75. I COME now to the description of the common quahties i 
of monads. The first of these are perception and appetition. i 
That monads must have perceptions is proved in various ways. 
(1) (D. 209 ; L. 407 ; G. vi. 598) Monads " cannot have shapes ; 
otherwise they would have parts. And consequently a monad, 
in itself and at a given moment, cannot be distinguished 
from another except by its internal qualities and actions, which 
cannot be other than its perceptions (that is to say, representa- i 
tions of the compound, or of what is outside, in the simple) 
and its appetitions (that is to say, its tendencies to pass from 
one perception to another), which are the principles of change." 
That is, owing to the Identity of Indiscernibles, monads must 
differ; but since they have no parts, they can only differ in 
their internal states ; and internal states, as far as experience 
goes, are either perceptions or appetitions. (2) There is 
another argument of a more dynamical nature (D. 210; L. 409 ; 
G. VI. 599). " Since the world is a plenum all things are 
connected together, and every body acts upon every other, 
more or less, according to their distance, and is afifected by the 
other through reaction. Hence it follows that each Monad 
is a living mirror, or a mirror endowed with inner activity, 
representative of the universe according to its point of view." 
Leibniz could not evidently employ this argument to prove 
that he himself has perceptions, since these, according to such 
a system as his, are presupposed in Dynamics. Thus the proof 

9—2 



132 THE NATURE OF MONADS IN GENERAL. 

that all monads have perceptions presupposes that oneself has 
them, and this remains a premiss. What is proved is that 
everything else consists of similar substances with similar 
perceptions. 

That Leibniz himself had perceptions, or, if you prefer it, 
that there is a world not oneself or one's predicates, was never 
deduced by him from any further principle. "Souls know 
things,'' he says, "because God has put in them a principle re- 
presentative of things without" (D. 251; G. vir. 375. Of 
D. 275-6; G. vii. 410). "What is miraculous, or rather mar- 
vellous is that each substance represents the universe from its 
point of view " (G. III. 464). Perception is marvellous, because 
it cannot be conceived as an action of the object on the 
percipient, since substances never interact. Thus although it 
is related to the object and simultaneous with it (or approxi- 
mately so), it is in no way due to the object, but only to the 
nature of the percipient. Occasionalism prepared thfe way for 
this view by the doctrine that the mind perceives matter, 
I though the two cannot interact. What Leibniz did, was to 
' extend to an infinite number of substances the theory invented 
1 for two only (D. 275-6 ; G. vii. 410). 

As to the meaning of perception, it is " the expression of 

plurality in a unity (I' expression de la multitude dans I'unitd ") 

! (G. III. 69). As to what is meant by expression, Leibniz is very 

definite. "One thing expresses another," he says, "...when 

1 there is a constant and regular relation between what can be 

i said about the one and the other. It is thus that a projection 

in perspective expresses its original. Expression is common to 

all forms, and is a genus of which natural perception, animal 

feeling, and intellectual knowledge are species. In natural 

perception and in feeling it suffices that what is divisible and 

material, and dispersed among several beings, be expressed or 

represented in one indivisible being, or in a substance endowed 

[with a true unity" (G. ii. 112). Again Leibniz says: "It 

is not necessary that what expresses be similar to the thing 

i expressed, provided a certain analogy of conditions is preserved 

And so the fact that ideas of things are in us is nothing 

else than the fact that God, the author alike of things and 
the mind, has impressed a faculty of thought upon the mind, 



THE NATUEK OF MONADS IN GENERAL. 133 

such that out of its own workings it can draw what perfectly 
corresponds to what follows from the things. And so, although 
the idea of the circle be not similar to the circle, yet from it 
truths can be drawn which in the true circle experience would 
no doubt have confirmed" (N. E. 716-7; G. vil. 264). Thus 
perception might seem to be hardly distinguishable from the 
pre-established harmony, and to amount only to the assertion 
that every state of a monad corresponds, according to some 
law, with the simultaneous state of every other monad : and it 
is thus that, as I suggested at the end of Chapter X., 
simultaneity is involved in the definition of perception. There 
is, however, one element in perception, namely the synthesis or 
expression of the multitude, which is not involved in the pre- 
established harmony alone ; and this element accordingly must 
be remembered and emphasized. 

76. As regards appetition, there is little to say beyond 
what was said about the activity of substance. "Appetite is 
the tendency from one perception to another " (G. iii. 575). It 
is conceived on the analogy of volition. The nature of sub- 
stantial forms, Leibniz says, is force, which involves something 
like sensation or desire, so that they become similar to souls 
(D. 72 ; L. 301 ; G. iv. 479). Perceptions in the monad spring 
from one another according to the law of appetites, or by the 
final causes of good and evil (D. 210 ; L. 409 ; G. vi. 599). 
Only volition, however, which is confined to self-conscious 
monads, is definitely determined by the fact that the object of 
desire seems good. This point, on which Leibniz is somewhat 
vague, will be treated later. 

77. Leibniz's theory of perception is rendered peculiar by 
the fact that he denies any action of outside things upon the 
percipient. CHis theory may be regarded as the antithesis of 
Kant's^ Kant thought that things in themselves are causes (or~ ". 
groiyias) of presentations, but cannot be known by means of 
presentations \ Leibniz, on the contrary, denied the causal ' v. 
relation, but admitted the knowledge. His denial of the . 
causal relation was, of course, due to his general denial of 
transeunt action, which, as we saw, was due to his conception 

of an individual substance- as -eternally— eonta3Eing^al"l_ itS- 
' E.g. Eeine Fc»-TOn/f,rBd7-Hartenstein7i867, p. 349. 



134 THE NATURE OF MONADS IN GENERAL. 

predicates . " I do not believe," he says, " that any system is 
possible in which the monads interact, for there seems no 
possible way of explaining such action. Moreover, such action 
would be superfluous, for why should one monad give another 
what the other has already ? For this is the very nature of 
substance, that the present is big with the future" (G. li. 503). 
His first somewhat tentative expression of the mutual inde- 
pendence of substances, in January 1686, is interesting as giving 
very clearly his grounds for this opinion. " We may say, in 
some manner, and with a good sense, though not according to 
usage, that a particular substance never acts on another 
particular substance, and does not suffer from it either, if we 
consider that what happens to each is only a consequence of its 
idea or complete notion quite alone, since this idea already 
contains all its predicates or events, and expresses the whole 
universe." He proceeds to explain that nothing can happen to 
us but thoughts and perceptions, which will be consequences 
of the present ones. ''If I could see distinctly all that is 
happening to me now, I could see all that ever will happen to 
me, and this would happen though all were destroyed but God 
and me " (G. iv. 440). 

This theory of perception has, no doubt, a paradoxical 
appearance. It seems absurd to suppose that knowledge of 
what is going on outside me should arise in me simultaneously 
with the external event, unless there is some causal connection 
between the two. But to the theory that external objects act 

! on the mind and produce perceptions there are many objections. 
One of these is that such an explanation does not apply to the 
knowledge of eternal truths. We cannot suppose that the 
proposition " two and two are four " acts on the mind whenever 
the mind is aware of it. For a cause must be an event, and 
this proposition is not an event. We must admit, therefore, 
that some knowledge is not caused by the proposition which is 
known. There seems no reason, when this is admitted, to deny 
that all knowledge may be otherwise caused. Leibniz does not, 
so far as I know, expressly use this argument, but his special 

I anxiety in the first book of the New Essays to prove that 
eternal truths are innate may be connected with some such 

! view. For according to his theory, all knowledge is innate in 



THE NATURE OF MONADS IN GENERAL. 135 

the same sense as the eternal truths, i.e. all knowledge springs 
from the nature of the mind, and not from the objects of sense. 
The argument which Leibniz does use is a better one, namely 
the unintelligibility of any such causal action as is ascribed to 
objects of sense. " I don't assent," Leibniz says, " to the vulgar 
notions that the images of things are conveyed by the organs of 
sense to the soul. For it is not conceivable by what aperture or 
by what means of conveyance these images can be carried from 
the organ to the soul " (D. 275 ; G. vii. 410). Indeed it is 
only necessary to state these notions in order to see how very 
" vulgar " they are. But when Leibniz goes on to say, in 
agreement with the Cartesians, that "it cannot be explained 
how immaterial substance is affected by matter'' (D. 276; G. 
■VII. 410), he is employing an argument which doubtless greatly 
influenced the formation of his theory, but which, none the less, 
he has not the slightest right to employ. For as he holds that 
there are only monads, perception, if it were caused from with- 
out, would still be an action of like upon like, and not, as he 
suggests, an action of mere matter upon the mind. The relation 
of mind and body, in fact, is a relation between many monads, 
not between two radically different substances, mind and 
matter. 

78. Lotze has given, in his Metaphysic (§§ 63-67), a 
criticism of the independence of monads, which seems to me to 
show a radical misconception of Leibniz's grounds. " I cannot 
admire," he says (§ 63), " this expression (that monads have no 
windows), because I find it quite unmotived, and find that it 
curtly excludes just what was still in question." If Lotze 
had remembered the array of logical arguments set forth in 
Chapters II. — IV. above, proving that, if there be substances at 
all, each must be the source of all its predicates, he could 
hardly have made this statement. If he had remembered his 
own philosophy — how, in the very next chapter (Bk. I. Chap. VI.) 
he has to abandon plurality of things on the explicit ground 
that transeunt action is unintelligible — if he had remembered 
that, in his own teaching, the unity of a thing is essentially the 
unity of one causal series — if all or any of these considerations 
had been in his mind, he would have spared his own glass house, 
and not ventured on throwing stones. And when we consider 



136 THE NATURE OF MONADS IN GENERAL. 

that a thing for him is a single causal series, the absurdity of 
allowing interaction of things becomes a direct contradiction. 
The antinomy of causation — that every element of the present 
must have its effect, while yet no effect can be afKrmed without 
taking account of the wliole present — this antinomy, I think, is 
one on which he was never clear. He contents himself with 
asserting first the thesis, while he is concerned with plurality, 
and then the antithesis, when he comes to his M, his unity. 
But to assert, as he does, that two causal series can interact, 
is a direct contradiction, and one which, even if it embodies a 
real antinomy, a man can hardly be called absurd for denying. 
I Lotze's criticism of Leibniz, therefore, seems due rather to his 
1 own confusion of thought, than to any error in Leibniz. There 
is as good ground for Monadism as for Monism, and a Monadist 
must, with Leibniz, maintain the mutual independence of sub- 
stances. 

79. To explain how perceptions give knowledge of present 
external things, though not due to these things, Leibniz 
invented the crowning conception of his philosophy, the con- 
ception by which he denoted his system. He loved to call 
himself "the author of the system of the pre-festablished 
>•; harmony." The pre-established harmony is that in his 
I philosophy of which he seems to have been proudest. Like 
the mutual independence of substances, this was doubtless 
I suggested by the course of Cartesian philosophy. The simile 
I of the clocks, by which he illustrated it, is to be found in 
Geulincx and other contemporary occasionalists, and even in 
\ Des Cartes'. The relation of thought and extension in Spinoza 
is very similar to that of any two monads in Leibniz. The 
advantage which he had over occasionalism, and of which he 
made the most, was that by the activity of every substance he 
was able to preserve the harmony of all the series without the 
perpetual intervention of God. This advantage was already 
secured in Spinoza, but not in occasionalism such as that of 

' See Ludwig Stein, Zur Genesis des Occasiormlistims, Archiv fur Gesch. der 
Phil., Vol. I.; esp. p. 59, note. Leibniz has been accused of stealing this 
illustration from Geulincx, but Stein points out that it was so common as to be 
obtainable from many other sources, and not to require special acknow- 
ledgment. 



THE NATURE OF MONADS IN GENERAL. 137 

Malebranche. It was there held that, since matter is essentially 
passive, the changes in matter corresponding to those in mind 
must be effected by the direct operation of God in each case. 
In Leibniz, on the contrary, only one original miracle was 
required to start all the clocks (G. ill. 143) — the rest was all 
effected naturally. We may suppose that Leibniz began with | 
the Cartesian problem of the harmony of soul and body, and ; 
found in his doctrine of monads a far wider harmony by which 
far more was explained. The pre-established harmony, he ' 
thinks, is proved cb priori : only three explanations of the 
relation of soul and body are possible, and of the three his is 
the best (G. III. 144). The other two are, of course, the 
influxus physicus or direct causal action, and the system of 
occasional causes, i.e. the action of God upon matter on occasion 
of every volition. As long as the perfect passivity of matter i 
was maintained, Leibniz's hypothesis certainly w^as the best. I 
But the systems of Geulincx and Spinoza, which he leaves out 
of account in this connection (Geulincx, in fact, is never 
mentioned, and seems to have been unknown to him), have 
many of the advantages in this problem which he claims as 
peculiarly his own. It is interesting to compare, for instance, 
the enunciation of Prop. XII. Part II. of Spinoza's Ethics : 
" Whatever happens in the object of the idea constituting the 
human mind must be perceived by the human mind, or, in 
other words, an idea of that thing will necessarily exist in the 
human mind. That is to say, if the object of the idea con- 
stituting the human mind be a body, nothing can happen in 
that body which is not perceived by the mind." From such a 
theory it is evident that Leibniz may have 'derived many 
suggestions for his theory of perception and pre-established 
harmony. It is to be regretted, therefore, that he did not take 
more account of this more allied hypothesis. 

The pre-established harmony is an immediate result of 
perception and the mutual independence of monads. " The 
nature of every simple substance, soul, or true monad," Leibniz 
explains, " being such that its following state is a consequence 
of the preceding one ; here now is the cause of the harmony 
found out. For God needs only to make a simple substance 
become once and at the beginning a representation of the 



138 THE NATURE OF MONADS IN GENERAL. 

universe, according to its point of view ; since from thence alone 
it follows that it will be so perpetually ; and that all simple 
substances will always have a harmony among themselves, 
because they always represent the same universe" (D. 278; 
G. VII. 412)'. iSach monad always represents the whole 
universe, and therefore the states of all monads at every 
instant correspond, in that it is the same universe they 
represent. To this Lotze objects that some monads might run 
through their series of perceptions faster or slower than others 
(Met. § 66). To this difficulty, he says, he remembers no 
answer in Leibniz. He appears to have forgotten that Clarke 
raised precisely the same point (G. vii. 387-8) and that 
Leibniz replied to it (G. vii. 415 and D. 281). " If the time is 
greater," he says, " there will be more successive and like states 
interposed ; and if it be less, there will be fewer ; seeing there 
is no vacuum, nor condensation, nor penetration (if I may so 
I speak) in times, any more than in places." That is to say, just 
as the quantity oi materia prima is proportional to extension, so 
I the number of events is proportional to time. Whatever may 
! be thought of this answer, it is evident that the monads, if 
j each of them mirrors the present state of the universe, neces- 
Isarily keep pace with one another. It is better, perhaps, to 
start with perception, and deduce the pre-established harmony. 
For some arguments can be adduced, if it be admitted that 
we have perceptions of an external world, to show that this 
is also true of other substances ; and hence the pre-estab- 
lished harmony follows. 

It remains to explain, in terms of monads, the relation of 
soul and body-, and the activity and passivity of substances. 
This will be attempted in the next chapter. 

1 Of. also G. I. 382-3. 



139 



CHAPTER XII. 

SOUL AND BODY. M- 'i V 7 J 

80. I PASS now to an entirely new department of the 
doctrine of monads. Hitherto we have considered single 
monads as isolated units, but we must now attend to their 
relations. We have to consider, in fact, the same problem as 
that which, in a dualistic system, would be the relation of 
mind and matter. The special form of this problem, which is 
usually considered, is the relati on of Soul and Body, In dis- ' 
cussing this relation, Leibniz introduced a new idea, that of 
passivity. This idea, it is true, was already involved in materia 
prima, but there it was not, as in the theory of soul and body, 
relative to the activity of some other monad. Byjthis relation, 
both activity and passivity acquire ne^v meanings. From this 
point onwards, Leibniz's philosophy is less original than hereto- 
fore. Indeed he is chiefly engaged in adapting to the doctrine 
of monads previous theories (notably' that of Spinoza), which, 
by means of the relation of activity and passivity, become 
available for him in spite of the denial of transeunt action. 
Thus a sharp line should, I think, be drawn between those ; 
parts of Leibniz's philosophy which we have hitherto discussed, 
and those which, through passivity, depend upon the apparent 
interaction of monads. The former seem mainly original, while 
the latter are borrowed in great part, though always without 
acknowledgment, from Spinoza. 

81. The problem of the relation of Soul and Body was one 
which occupied much of the attention of Cartesians. Des 
Cartes' own position on this question, that a direct action of 
mind on matter is possible, by altering the direction, though 



140 SOUL AND BODY. 

not the quantity, of the motion of the animal spirits, was aban- 
doned by his followers for very good reasons. They perceived 
that, if mind and matter are two substances, they must not be 
supposed capable of interaction. This led to Occasionalism on 
the one hand — the theory, namely, that God moves the bodj' on 
occasion of our volitions — and to the theory of Spinoza on the 
other hand. In this latter theory, which is more akin to 
Leibniz's, mind and body are not different substances, but 
different attributes of one substance, whose modifications form 
two parallel series. The mind is the idea of the body, and any 
change in the body is accompanied, though without inter- 
action, by a corresponding change in its idea, i.e. in the mind. 
This theory, as well as that of the Occasionalists, was rendered 
impossible for Leibniz by the discovery that the essence of 
matter is not extension, but that matter is necessarily plural. 
! Accordingly he required a new theory of Soul and Body, and 
this requirement was doubtless a main motive to the doctrine 
of pre-established harmony \ The use of this doctrine in 
explaining the relation of Soul and Body is most ingenious. 
I shall now endeavour to set it forth. 

82. Briefly, the doctrine is as follows. Since there is 
nothing real but monads, the body is the appearance of an 
infinite collection of monads. But monads differ in the clear- 
ness of their perceptions, and those which have clearer percep- 
' tions are more active. When a change in one monad explains 
a change in another, the first is said to be active, the second 
passive. So, in my body, that monad which is myself has 
clearer perceptions than any of the others, and may be said to 
be dominant in the body, since, in relation to the other monads, 
it is active while they arc passive. There is no real interaction, 
but the appearance of it results from the pre-established har- 
i mony. Thus the soul is one, the body many, and there is no 
interaction between them. But in so far as the soul has , clear 
perceptions, the reasons for what happens in the body are to be 
found in the soul ; and in this sense the soul acts on the body 
and dominates it. This is the outline of the theory which must 
now be examined in detail. 

1 In Wolff's philosophy, the harmony of all monads has disappeared, and 
only that of soul and body remains. 



SOUL AND BODY. 141 

83. There are, in the first place, three great classes in the 
hierarchy of monads, not sharply distinguished, but merging 
into each other. These are bare monads, souls and spirits. 
Bare monads, which are also called forms or entelechies, have 
the minimum of perception and desire; they have something 
analogous to souls, but nothing that could strictly be called a 
soul. Souls are distinguished from the first class by memory, 
feeling, and attention (1). 190—1 ; G. VII. 529 ; D. 220 ; L. 230 ; 
G. VI. 610). Aj^ai^ls__^hMe_s(mls,--h\xi_men_J[iave_,spirits or 
ra tional souls . Spirits include an infinite hierarchy of genii 
and angels superiorJiiLinen, but not differing from him except 
in degree. They are defined by self-consciousness or appercep- 
tion, by the knowledge of God and eternal truths, and by the 
possession of what is called reason. Spirits do not, like souls, 
mirror onlj' the universe of creatures, but also God. They thus 
compose the City of God, in relation to which alone God 
properly possesses goodness [G. VI. 621-2 (D. 231 ; L. 267 — 8) ; 
contrast G. VI. 169]. Spirits also are immortal : they preserve 
moral identity, which depends on memory of self, while other 
monads are merely incessant, i.e. they remain numerically 
identical without knowing it. 

84. In relation to clearness of perception, monads are said 1 
to be active or passive*. We can still popularly speak of one 1 
substance acting on another, Leibniz says, when a change in 
the one explains a change in the other (D. 79; L. 317; G. iv. 
486). But " the domination and subordination of monads, con- 
sidered in the monads themselves, consists only in the degrees 
of their perfections" (G. ll. 451). " Modifications of one monad i 
are ideal causes of those of another, in so far as the reasons 
appear in one monad which led God in the beginning to 
arrange for modifications in the other " (G. ii. 475). (And so the : 
body depends upon the mind in this sense, that the reason of 
what happens in the body is to be found in the mind.) In so 
far, Leibniz continues, as the soul is perfect, and has clear per- 
ceptions, the body is subject to it ; in so far as it is imperfect, 
it is subject to the body (G. VI. 138)". Again he says that the 

^ This sense of activity must not be confounded with that which is essential 
to substance. 

^ Of. Spinoza's Ethics, Pt. V. Prop. X. 



142 SOUL AND BODY. 

creature is said to act externally so far as it is perfect, and to 
suffe7- from another in so far as it is imperfect. Action is there- 
fore attributed where perceptions are distinct, passion where 
they are indistinct. One creature is more perfect than another, 
when it contains what accounts d priori for what happens in 
the other, and in this way it is said to act on another. The 
influence of one monad on another is purely ideal, through 
God, who takes notice of the superior monad in regulating 
others [G. vi. 615 (D. 225 ; L. 245)]. (Every substance which 
passes to a greater degree of perfection acts, and one which 
passes to a lesser degree of perfection suffers.) In any sub- 
stance which has perception, action brings joy, while passion 
brings pain (G. iv. 441). 

The activity which is opposed to passivity is quite distinct 
from that which is essential to substance. " Taking action in 
metaphysical strictness," Leibniz says (N. E. p. 218 — 9 ; G. V. 
195), " as that which takes place in a substance spontaneously 
and from its own nature, whatever is properly a substance only 
acts, for everything comes to it from itself, after God, since it is 
impossible that one created substance should have influence on 
another. But taking action as an exercise of perfection, and 
passion as the contrary, there is action in true substances only 
when their perception (for I grant it to all) is developed and 
becomes more distinct, as there is passion only when it becomes 
more confused ; so that in substances capable of pleasure and of 
pain, all action is a step to pleasure, and all passion a step to 
pain." 

85. In this theory, which is full of reminders of Spinoza', 
there are two elements in what is active, namely perfection, and 
clearness of perception. (It is plain that Leibniz does not con- 
fuse these two elements, but regards them as necessarily 
connected.) He evidently thinks, moreover, that his usage will 
cover the cases which are ordinarily regarded as cases of action 
and passion respectively. But these ideas need some expla- 
nation, as does also the phrase " accounting d 'priori for what 
happens in another monad." The explanation, I think, is as 
follows. 

Only spirits are good or bad as ends in themselves: bare 
' Cf. e.g. Spinoza, Ethics, Bk. III. Prop. i. 



SOUL AND BODY. 143 

monads and souls are mere means to them. Now in spirits, 
volition is always determined by the reason of the good', i.e. we 
pursue what we judge to be the best possible". Hence we shall 
always act rightly if we always judge rightly (G. vii. 92)'. 
Accordingly, since right judgment depends upon clear percep- 
tion, we are more or less perfect according as we have more or 
less clear perceptions. In volition, where we are ordinarily said 
to be active, the passage to a new perception is perceived to be, 
what it always is really, determined from within, and our per- 
ception, therefore, is so far clear. But in sensation, where we 
are ordinarily said to be passive, the new perception falsely 
appears to come from without, and our perception is therefore 
confused. We do not perceive the connection with the previous 
perception, and are so far imperfect. Thus Leibniz's use of the 
words active and passive is not wholly disconnected from the 
popular use, though it would be unwise to see too close a 
relation. 

And thus the phrase " containing what accounts d priori 
for the changes in another monad," is to be understood in 
relation both to perfection and to clearness of perception. 
Owing to the pre-established harmony, the changes in different f 
monads are inter-related ; but the changes in inferior monads 
exist mainly for the sake of the correlated changes in spirits*. 
IThus the explanation by sufficient reason, or by final causes, of 
what happens in an inferior monad, is only possible. by taking 
account of some superior monad, in which the correlated change 
is good.) But when this superior monad is free, and owing to 
confused perception chooses what is really bad, this explanation 
by final causes no longer holds, and the superior monad is 

1 G. IV. 454; v. 171 (N. E. 190-1); F. de C. 62 (D. 182). 

''■ It is thus, by the way, that actual sufficient reasons of the actual are 
distinguished from possible sufficient reasons of the possible. All actual 
sufficient reasons are volitions either of God or of free creatures, and these are 
always determined by the (true or false) perception of the good. But it would 
be possible, not only for us, but also for God, to pursue evil, and then the per- 
ception of evil would be a sufficient reason. Thus actual sufficient reasons are 
final causes, and involve reference to the good. Cf. § IS, supra. 

' That this view was often contradicted by Leibniz (e.g. implicitly, ib. p. 9S) 
was only due to theological reasons. It was the only view to which he was 
entitled, 

* For Leibniz's inconsistency on this point see § 124. 



144 SOUL AND BODY. 

therefore regarded as passive, since the final reason of its 
change for the worse is not in itself, but in some correlated 
change elsewhere. 

86. There are, in the above theory, many obvious gaps, 
•which I leave without comments It is more important to 
explain the connection of passivity and materia prima. Leibniz 
distinguishes in one place (G. il. 252) the following five terms : 
"(1) The primitive entelechy or soul, (2) primary matter or 
primitive passive power, (3) the monad composed of these two, 
(4) mass or secondary matter or the organic machine, to which 
innumerable subordinate monads concur, (5) the animal or 
corporeal substance, which the dominant monad makes into 
one machine.'' Moreover the connection of soul and body is 
only explicable by means of materia prima\ Hence we must, 
before we can understand the connection of soul and body, 
examine the nature of materia prima as an element in each 
monad, and its connection with m,ateria prima in Dynamics. 
' Materia prima, as an element in each monad, is that whose 
repetition produces the materia prima of Dynamics. It is also 
identified with the passivity or passive force of each monad, 
i with confused perception, and with finitude generally. God 
could deprive a monad of materia secunda, i.e. of the assemblage 
I of monads which constitutes its body ; but He could not deprive 
! a monad of materia prima, without which it would be actus 
i purus, i.e. God Himself (G. ii. 325). It is thus by materia 
prima that monads are distinguished from God, and rendered 
' limited and finite ; and this seems to be Leibniz's meaning in 
saying that confused perceptions are what involve matter or 
the infinite in number (G. iii. 636). In writing to Arnauld, 
Leibniz says : " If we understand by matter something always 
essential to the same substance, we might, with some scholas- 
tics, understand by it the primitive passive power of a sub- 
stance, and in this sense matter would be neither extended nor 

• The chief of these is that there seems no reason why action in one 
substance should correspond to passion rather than action in another. Leibniz 
seems indeed to regard it as more or less accidental when this occurs ; thus he 
says (G. iv. 440): "It may happen that a change which Increases the expression 
of the one diminishes that of the other." 

2 G. II. 520, 248; vi. 546 (D. 169). 



SOUL AND BODY. 145 

divisible, though it would be the principle of divisibility, or of 
that, in it, that belongs to substance" (G. ii. 120) (1687). This 
is, I think, the first time that he introduces into the theory of 
monads materia prima in the sense given it by " some scholas- 
tics," and it has the tentativeness of a new idea. But to this 
sense he afterwards always adheres. Materia prima, he says, 
is not extended, but is what extension presupposes. It is the 
passive power which, with the entelechy or active power, com- 
pletes the monad, and it adheres always to its own monad'. 
Substances have metaphysical matter or passive power in so far 
as they express anything confusedly ; they have active power in 
so far as they express anything distinctly (N. E. 720; G. vil. i 
322). Monads are subject to passions, and are thus not pure 
forces ; they are the foundations not only of actions, but also of 
resistances and possibilities, and their passions are in confused 
perceptions (G. III. 636). For substance acts as much as it 
can, unless it is impeded; and it is not impeded naturally 
except from within. When one monad is said to be impeded 
by another, this is to be understood of the representation of 
that other in itself (G. II. 516). Moreover it is not absurd, 
Leibniz thinks, that resistance in a substance should do nothing 
but impede its own activity; we need, he says, a principle of 
limitation in limited things, as of action in agents (ih. 257). 

87. Several things are interesting and noteworthy in this 
theory of materia prima. First, it is instructive to observe t 
the difference between Leibniz's account of limitation and that 
of Spinoza. " That thing is called finite in its own kind," 
Spinoza says (Eth. I. Def 2), " which can be limited by another 
thing of the same nature." Thus finitude consists in a relation ' 
to something else, and the finite is not self-subsistent. But "" 
Leibniz's materia prima is nothing relative, but part of the > 
nature of each monad. Each monad is limited, not by some- i 
thing else, but by itself^; and thus God is not the sum of finite 

1 G. n. 306 ; cf. also G. iv. 511 (D. 120). 

2 Cf. Erdmann, Grundriss der Geschichte der Philosophie, 3rd ed. Berlin, 1878, 
Vol. II. p. 150. In a highly interesting paper, which is very Spinozistic through- 
out, and belongs probably to the period between 1676 and 1680, Leibniz actually 
gives Spinoza's definition of finitude as his own: "The finite involves negation 
of something of its own kind" (G. vii. 196). He proceeds to remark, however, 
that this definition seems inapplicable to discreta. 

R. L. 10 



14fa* SOUL AND BODY. 

monads, but something radically different in his nature. Con- 
nected with this point is the way in which passivity involves 
[matter and the infinite in number (G. ill. 636). There is only 
one way of perceiving the world clearly, namely the way in 
;i which God perceived it, i.e. as it really is. But there is an 
i infinite number of ways of perceiving it confusedly. Thus the 
Identity of Indiscernibles allows only one God, and is only 
compatible with many other substances if these all have per- 
ceptions which are more or less confused. And as matter is 
the confused perception of an infinite plurality of monads, 
matter doubly presupposes materia prima, namely as the source 
of the plurality, and again as the reason why the plurality is 
perceived as matter. And this brings us to the relation of the 
materia prima in each monad to the materia prim,a in Dy- 
namics. fThe two elements in the dynamical definition — 
impenetrability and inertia — correspond respectively, I think 
(though this is only an inference), to the fact that monads 
differ as to their point of view, and the fact that passivity 
causes a resistance to a new perception in the monad. Both 
I these are included under confused perception.) God, who alone 
I sees quite clearly, has no point of view — space, to him, is as it 
5 is in Geometry, without any here or there. All points are alike 
i in their relation to God (G. iv. 439 ; ii. 438), and the same 
I must be true of the parts of time. Thus the point of view is a 
1 part of confused perception, and therefore of materia prima; 
I and the difference of points of view is the source of impenetra- 
«} bility. Similarly, owing to passivity or indistinctness of per- 
ception, a given perception does not give rise to the perception 
which would result if the same thing were more clearly per- 
ceived ; and this, we may suppose, is the source of inertia. 
There is, however, a difference between the dynamical use of 
materia prima and the use in the theory of monads, namely 
that, in Dynamics, the word is usually applied to a finite 
extension, resulting from an infinite number of monads, whereas 
in the theory of monads it is applied to the corresponding 
quality of each monad, i.e. to that quality whose repetition is 
required to produce extension. 

88. The connection of confused perception with the point 
of view explains also some rather difficult dicta on the inter- 



SOUL AND BODY. 147 

connection of monads. "If there were only spirits," Leibniz i 
says, " they would be without the required connection, without ' 
the order of times and places. This order demands matter and 
motion and its laws " (G. vi. 172). God alone is above all , 
matter ; creatures free from matter would be deserters from the 
general order, and detached from the universal concatenation 
(D. 169 ; G. VI. 546). Again Leibniz pronounces against the 
view that angels are disembodied spirits. To remove them | 
from bodies and from place, he says, is to remove them from 
the universal connection and order of the world, which is made 
by relations to time and place (G. il. 324). All these sayings 
seem explained by the fact that places result from points of 
view, and points of view involve confused perception or materia 
prima. And this, again, is intimately connected with the 
doctrine of unconscious perception, which Leibniz urged with 
such success against Locke. To maintain that we mirror the ; 
whole universe was only possible by a large use of this doctrine. 
And Leibniz did, in fact, carry the doctrine so far as to main- 
tain that every perception of which we are sensible is composed 
of an infinite number of insensible perceptions (N. E. 116 — 8: 
G. V. 105 — 7). He once even deduces the infinite number of 
monads from this consideration alone. In our perceptions, he 
says, however distinct they may be, there are confused ones to 
any degree of smallness, and to these, as to the greater and 
more distinct ones, monads will correspond (G. II. 460 — 1). 

89. We can now endeavour to understand the connection i 
of soul and body. There are here, I think, two inconsistent 
theories, both contained in Leibniz. This has led to a division 
among commentators, some insisting on the one as the only 
theory, others on the other. As I have found no way of recon- 
ciling all Leibniz's statements on the matter, I shall first set 
forth the theory which seems to me consistent with the rest of 
his philosophy, and shall then proceed to the second theory, 
showing why it cannot be reconciled with his other views, and 
how he seems to have been led to it. The first theory has been 
supported by Erdmann, the second by Kuno Fischer, in whose 
histories the arguments will be found at length. 

90. We must, to begin with, distinguish an organic body ' 
from a mere mass. An organic body has one dominant monad, 

10-^3 " 



148 SOUL AND BODY. 

^h j relation to which it acquires a certain unity. It is as 

regards the nature and degree ot this unity that the two 

theories differ. An inor ganic bod y has n o such single domi- 

nant mon ad, but is a mere aggregate' . But eve ry mo nad 

belongs to so7 ne organic b ody, either as dominant or as subo rdi- 

nate monad^. Every orga nic body is c om posed "f an infinite 

n"umFer of smaller organic bodies, the smallest organic bodies 

occupying only a physical point. A natural machine, Leibniz 

says, is a machine even in its smallest perceptible parts [G. VI. 

599 (D. 209 ; L. 408); G. ii. 100 ; iv. 492]. ( In the firjt theory, 

the dominant m onad dominate s in the sense that it represents 

more clea rly what the other mona ds re present- s mry nnnfnnnd ly. ) 

In accordance with the affections of the body, the dominant 

monad represents, as a centre^ the things outside itself [G. vi. 

f 598 (D. 209 ; L. 407)]. Leibniz is not very definite as to the 

; meaning of domination, but the following seems to be his 

meaning. Every mon ad perceives more clearly what hap pens 

in its neighbour hood than wha t h a pp rn n nt a d intanrp [G. II. 

: 74 ; %rTir59^~(Dr2107K409)]. If, then, in a certain 

volume, there is one monad with much clearer perceptions than 

the rest, this monad may perceive all that happens within that 

volume more clearly than do any of the others within that 

' volume. And in this sense it may be dominant over all the 

, monads in its immediate neighbourhood. 

* j But we must not suppose that the monads composing the 

I organic body are always the same. There is not a portion of 

matter, i.e. of inferior living beings, appropriated to the soul for 

I ever, for bodies are in perpetual flux. The soul changes its 

I body, but always gradually [G. VI. 619 (D. 229; L. 258)]. 

Thus we cannot be certain that the smallest particle of matter 

(i.e. secondary matter) received by us at birth, remains in our 

'• body. But the same animal or machine subsists in a sense 

: [G. VI. 543 (D. 167)] ; it persists, as Leibniz puts it, specifically 

: but not individually [G. v. 214 (N. E. 240)]. Certain organs 

remain, at least by the substitution of an equivalent, as a river 

remains the same though its matter changes (G. iv. 529). 

This is merely the ordinary scientific view, according to which 

J G. VI. 539 (D. 163) ; G. v. 309 (N. E. 362); G. ii, 75, 100. 
2 G. II. 118, 135; III. 356; vii. 602. 



SOUL AND BODY. 149 

the body remains of the same kind, though not composed of 
the same matter. Thus the body consists merely of those 
inferior monads whose points of view, at any given time, are so 
near that of the dominant monad that they perceive everything 
less clearly than it does, since every monad perceives most 
clearly what is in its own neighbourhood. Body an d soul do 
not together form one snbsta.ncp. (G. vi. 595), an d do not even 4 



interact. " "Rndiea act as if ( what is impossible) th ere were no \ 
souls, and souls act as if there were no bodies, and both act as 
if t he one influenced the other" |(i . Yi. 621 (P. 230 ; L. 264)]. 
The organized mass, within which is the point of view of the 
soul, is ready to act of itself, at the moment when the soul wills 
it. This, Leibniz says, produces the so-called union of soul and 
body [G. IV. 484 (D. 78; L. 314)]. Soul and bod y__donot 
i nteract, but only agree, the o ne acting freely, according to t he 
rules of final causes, the othe r acting mechanical ly, according 
to t he laws of efficient cause s. But this does not derogate from 
the liberty of the soul. For every agent which acts according 
to final causes is free. God, foreseeing what the free cause 
would do, regulated the machine to agree with it [G. Vil. 412 
(D. 278)]. 

This, then, is the first theory of soul and body. An organic | • 
body is a collection of changing monads, which acquires unity ; 
by being always subject to one and the same dominant monad. 
This subjection consists both in the clearer perceptions of the 
dominant monad, and in the fact that the final causes, which 
govern all events, have reference, so far as the body is con- 
cerned, either to the dominant monad, or to some monad 
outside the body, or to "metaphysical perfection" and the 
"order of things." A body dominated by a spirit consists of 
innumerable smaller organic bodies, but does not itself, ap- 
parently, form part of any larger organic body. Secondary 
matter, or mass, consists of a collection of organic bodies not 
unified by one dominant monad. (There are, however, many 
things in Leibniz inconsistent with this simple theory. To 
these we must now turn our attention.) 

91. Though everything in the above theory, as I set it < 
forth, is to be found in Leibniz, there are many other passages, 
concerning which I said nothing, which lead to a totally dif- 
ferent theory. This theory is to be rejected, I think, because 



150 SOUL AND BODY. 

I it is wholly inconsistent with Leibniz's general philosophy. 
j But it is necessary to say something about it, particularly 
as it has been supported, with constant appeal to the sources, 
i by a recent commentator, Dillmann'. 

j In this other theory, mind and body together make one 
j substance, having a true unity. The mind makes the body 
I into a unum per se, instead of a mere aggregate. Against this 
view, we have perfectly definite assertions, such as the following 
(D. 177 ; F. de C. pp. 32, 34) : " Corporeal substance has a soul 
and an organic body, that is, a mass made up of other sub- 
stances. It is true that the same substance thinks, and has 
an extended mass joined to it, but it does not consist of this 
mass, since all this can be taken away from it without altering 
(the substance." Nevertheless, in other places, Leibniz speaks 
I as if the soul and the body mak^ one substance. 

" The entelechy," he says, " is either a soul, or something 
analogous to a soul, and always naturally actuates some organic 
body, which taken by itself, apart from the soul, is not one 
substance, but an aggregate of several, in a word, a natural 
' machine" (G. iv. 395—6; N. E. 701) (1702). Again he says: 
"Every created monad is endowed with some organic body" 
(G. VII. 502), " principles of life belong only to organic bodies " 
[G. VI. 539 (D. 163)], and again : " There are as many entele- 
chies as organic bodies" (G. ii. 368). It is evident that not 
every monad can have an organic body, if this consists of other 
subordinate monads. And there are many more direct reasons 
for the view that body and soul together make one substance. 
" Bodies which are a unum per se, like man," Leibniz says, " are 
substances, and have substantial forms" (G. IV, 459) (Jan. 1686). 
And Leibniz always speaks as if the presence of the soul pre- 
vented the body from being a mere aggregate : he suggests 
that the body without the soul is a mere aggregate, but with it, 
acquires a true unity. " The number of simple substances," he 
says, " in any mass, however small, is infinite ; for beside the 
soul, which makes the real unity of the animal, the body of the 
sheep, for example, is actually divided, i.e. is an assemblage 
of invisible animals or plants, similarly composite except for 
what makes their real unity ; and though this goes to infinity, 

1 Eine neue Darstellung der Leibnuischen Monadenlehre auf Grund der 
Quellen. Leipzig, 1891. 



SOUL AND BODY. 151 

it is plain that all in the end depends on these unities, the 
rest, or the results, being only well-grounded phenomena " 
(G. IV, 492). This tendency is carried farthest in a theory r 
which has given commentators much trouble, but is really no '■f- 
more inconsistent with Leibniz's system than many other pas- 
sages — I mean the doctrine of the vinculum substantiale. 

92. This doctrine is developed in the letters to Des | 
Bosses, and springs from Leibniz's endeavour to reconcile his | 
philosophy with the dogma of transubstantiation. (, It is neces- : 
sary to find some sense in which the Body of Christ is one 
substance.) Leibniz first admits "a certain real metaphysical 
union of soul and organic body" (G. II. 371), an admission he 
had already made to Tournemine (G. VI. 595), but Des Bosses 
persuades him that this is not sufficient for Catholic orthodoxy. 
He then suggests, as a view which he does not acQspt, but [ 
which might be helpful to a good Catholic, the hypothesis of j 
a substantial bond (G. Ii. 435). " If corporeal substance," he I 
says, "is something real beside monads, as a line is held to 
be something beside its points, we shall have to say, that 
corporeal substance consists in a certain union, or rather in 
some real thing which unites, and is added by God to the 
monads; that from a certain union of the passive power of 
monads materia prima results, that is, what is required by 
extension and antitypia, or diffusion and resistance ; but that, 
from the union of the entelechies of monads, a substantial form 
arises, but one which can thus be born and extinguished, and 
is extinguished when that union ceases, unless God miraculously 
preserves it. But such a form will not be a soul, which is a 
simple and indivisible substance^" This vinculum substantiale 
is only asserted to be useful " if faith leads us to corporeal 
substances " (ib.). And later he says (ib. p. 458) : " And this 
seems what should be said by people of your way of thinking 
{secundum vestros), of the change of the whole substance of 
one body into the whole substance of another body, which yet 
retains its former nature." The vinculum s-abstantiale differs i 
from the real union of soul and body — which Leibniz also 
admits elsewhere — by the fact that the monads are not added '■ 
as wholes to form a sum having a true unity, but are split j 
' Of. the schedule of all entities, G. n. 506. 



152 SOUL AND BODY. 

up into materia prima and entelechy before addition. Thus 
the sum of constituent elements of materia prima gives an 
extended passive mass, while the sum of the entelechies gives 
a substantial form animating the mass. There is one vinculum, 
substantiate for each organic body, i.e. one corresponding to each 
dominant monad (G. II. 481, 486, 496). Leibniz is afterwards 
led by Des Bosses to admit that this substantial bond must, if 
it is to be theologically serviceable, be imperishable like the 
individual soul (G. il. 481). In later letters, the doctrine is 
usually presupposed as the basis of discussion, and is employed 
to establish real matter and a real continuum. But nowhere 
does Leibniz himself assert that he believes it. He was ex- 
tremely anxious to persuade Catholics that they might, without 
heresy, believe in his doctrine of monads. Thus the vinculum 
substantiate is rather the concession of a diplomatist than the 
creed of a philosopher (cf G. ii. 499). 

93. It seems not impossible that others of Leibniz's re- 
marks, in so far as they are inconsistent with the first theory 
of body, are also due to theological influences. The problem 
of the Real Presence occupied Leibniz from the time when 
he was in the service of the Archbishop of Mainz, and formed 
one of his grounds for denying that the essence of matter is 
extension. In his earliest accounts of his system, designed for 
the zealous and proselytising Arnauld, similar suggestions are 
to be found. " The body by itself," Leibniz says, " apart from 
the soul, has only a unity of aggregation " (G. ii. 100) ; and 
this seems to imply that with the soul the body has a real 
unity. Again he says that the body, apart from the soul, is 
not properly a substance, but an aggregate, like a heap of 
stones {ib. 75). And when Arnauld objects to the new phi- 
losophy, that the soul joined to matter does not make one, 
since it gives only an extrinsic denomination, Leibniz replies 
that the matter belongs to the animated substance, which is 
veritably one being ; and matter taken only as mass is merely a 
well-founded phenomenon, like space and time {ib. 118). This 
might be understood as referring, in the first part, to materia 
prima, but the following passage is more difficult. "Those 
who will not admit," he says, " that there are souls in beasts, 
and substantial forms elsewhere, can nevertheless approve the 



SOUL AND BODY. 153 

way in which I explain the union of mind and body, and all 
that I say about true substance; but it remains to them to 
save, as they best may, without such forms, and without any- 
thing which has a true unity, either by points, or, if it seems 
good to them, by atoms, the reality of matter and of corporeal 
substances" (G. II. 127). Again he says that if there are no 
corporeal substances such as he wants, then bodies are merely 
true phenomena, like the rainbow. For, since matter is actually 
infinitely divided, we shall never reach a true being, save when 
we find animated machines, whose soul or substantial form 
makes a substantial unity independent of mere contiguity. 
And if there are none such, he concludes, then man is the 
only substantial thing in the visible world (G. II. 77). All 
these statements imply that soul and body together are veri- 
tably one, though the body alone, in so far as it is real, is 
many. In the letters to Arnauld, this might be attributed 
merely to the crudity of a new philosophy, but, as we have 
seen, there are many later expressions of a similar kind. And 
the doctrine which, in discussing the relation of monads to 
space (§ 71), we found inevitable, namely that the soul is present 
in a volume, not in a mere point, is to 'be associated with 
this view. The soul by its presence informs the whole body 
and makes it one, though other subordinate souls are present 
in various parts of the body, and make each such part one'. 
Again space, for Leibniz, is a plenum, but is not composed of 
mathematical points. Hence we must suppose every monad 
to occupy at least a physical point. Such a physical point 
might be called an organic body, and might explain how all 
monads come to have an organic body. The organic body of 
a monad which does not dominate would, by itself, be a pure 
phenomenon, and in no sense an aggregate. It is impossible, 
however, to free this view from inconsistencies. To these two 
causes may have contributed, the one the theological desire 
to save the reality of bodies^, the other an occasional confusion 

1 Of. the following (G. ii. 474): *'It is asked whether the soul of a worm 
existing in the body of a man is a substantial part of the human body, or rather, 
as I should prefer to say, a bare requisite, and something not metaphysically 
necessary, but which is only required in the course of nature." 

^ Thus in one passage Leibniz clinches his arguments by the remark: 
"Moreover the last Lateran Council declares that the soul is veritably the 
substantial form of our body" (G. ii. 75). 



154 SOUL AND BODY. 

of primary matter, as an element in each monad, either with 
primary matter as extended, or even with secondary matter. 
The latter may have been a partial cause in the letters to 
Arnauld ; in the letters to Des Bosses, the former must have 
operated alone, for the distinctions of the various kinds of 
matter are there more clearly drawn than anywhere else'. 

There may be a theory which accounts better for these 
apparent inconsistencies, but I have been unable to find one. 
I My theory is substantially that of Erdmann, to whom I may 
i refer for further discussion. 

j 94. A few words seem necessary about Preformation, the 
I theory by which Leibniz explained generation. As every 
monad is eternal, the monad which is myself must have pre- 
I viously existed. Leibniz holds that it formed one of the 
i monads composing the body either of father or mother 
1 (G. III. 565). Before conception, he thinks, it was either a 
mere sensitive monad, qt had at any rate only an elementary 
reason. The latter view has the advantage that it enables 
us to do without miracles. On the former view, since a 
sensitive monad cannot naturally become rational, we must 
suppose generation to involve a miracle. Leibniz cannot 
decide between these alternatives, indeed both are to be found 
I in the TModic6e^ (G. vi. 152, 352). It would seem that the 
I miraculous alternative is the best, because Leibniz wishes to 
[ maintain that human beings cannot naturally, after death, sink 
I to the level of mere sensitive monads ; but if monads can 
naturally become rational, there seems no reason why they 
■' should not naturally cease to be so. Leibniz supported his 
theory of preformation by reference to the microscopic em- 
bryology of his day. fit is, however, sufficiently evident that 
he could not account for the equal influence of both parents. 
When this is taken into account, we lose the simplicity of 
the one dominant monad, but we get a theory uncommonly 
! like Weissmann's continuity of the germ-plasm.) A few years 
ago, therefore, we might have referred to Leibniz as an- 
ticipating the latest results of modern science ; but since the 
, fall of Weissraann, we must deny ourselves this pleasure. 

1 See e.g. G. ii. 368, 370, 371. 

2 A fact which, by the way, supports Stein's contention that the parts were 
written at very different times: v. Leibniz und Spinoza, Berlin, 1890, p. 275 ff. 



155 



CHAPTER XIII. 



^'^ 



CONFUSED AND UNCONSCIOUS PERCEPTION. 

95. There are, we have seen, two respects in which 
monads differ. They differ as to point of view, and they differ 
as to clearness of perception. The first of these is continually 
changing : the reality underlying the phenomenon of motion 
is change of point of view. This seems to me, at least, the 
only possible interpretation, though Leibniz nowhere definitely 
makes this statement. In this way we should be able to 
interpret the difference between absolute and relative motion. 
The monad which changes its point of view has absolute 
motion, while another which perceives this change has only 
a relative change of situation *. This view again involves the 
objective counterpart to space, which we have seen throughout 
to be unavoidable. 

The point of view, as we have seen, depends upon con- 
fused perception, but not upon different degrees of confusion. 
As regards the degree of confusion, also, we must suppose 
change possible. Leaving aside the possibly miraculous change 
in conception, Leibniz could hardly maintain that babies have 
as clear perceptions as grown-up people. And he says that 
death, though it cannot entirely destroy memory, does render 
our perceptions confused [G. vii. 531 ; (D. 193)]. This is also 
his explanation of sleep. He maintains, against Locke, that the 
soul always thinks, but he confesses that it is not always con- 
scious of thought. We are never without perceptions, he says, 
but often without apperceptions, namely when we have no 
distinct perceptions (N. E. p. 166 ; G. v. 148). Thought is 

' Compare, on this subject, G. ii. 92 and iv, 513. 



156 CONFUSED AND UNCONSCIOUS PERCEPTION. 

the proper activity of the soul, and a substance once in action 
will be so always (G. V. 101 ; N. E. 111). If its activity ceased, 
the substance too, as we have seen, would cease, and on waking 
we should not be numerically the same as when we went to 
sleep. 

96. This brings us to a very important advance which 
Leibniz made in Psychology. Locke thought there could be 
nothing in the mind of which the mind was not conscious. 
Leibniz pointed out the absolute necessity of unconscious 
mental states. He distinguished between perception, which 
consists merely in being conscious of something, and apper- 
ception, which consists in self-consciousness, i.e. in being aware 
of perception [G. v. 46 (N. E. 47 ; L. 370); G. vi. 600 (D. 211 ; 
L. 411)]. An unconscious perception is a state of consciousness, 
but is unconscious in the sense that we are not aware of it, 
though in it we are aware of something else. How important 
these unconscious perceptions are, appears from the Intro- 
duction to the New Essays. It is in consequence of these 
that " the present is big with the future and laden with the 
past, that all things conspire, and that, in the least of sub- 
stances, eyes as penetrating as those of God could read the 
whole course of the things in the universe " (N. E. 48 ; L. 373 ; 
G. V. 48). They also preserve the identity of the individual, 
and explain the pre-established harmony ; they prevent an 
indifference of equilibrium (ih), and it is in virtue of them 
that no two things are perfectly alike (G, V. 49 ; N. E. 51 ; 
L. 377). 

In favour of unconscious mental states Leibniz has several 
arguments, some quite cogent, others, I think, depending upon 
confusions. Locke's argument, he says, that we cannot know 
anything which we are not aware of knowing, proves too much, 
for then we know nothing that we are not actually thinking 
of (G. V. 80 ; N. E. 84). Again, and this is the most conclusive 
argument, "it is impossible for us always to reflect expressly 
upon all our thoughts ; otherwise the mind would reflect upon 
each reflection to infinity, without ever being able to pass to a 
new thought. For example, in perceiving some present feeling, 
I should always have to think that I think of it, and again 
think that I think of thinking of it, and so on to infinity " 



CONFUSED AND UNCONSCIOUS PERCEPTION. 157 

(G. V. 108; N. E. 118—9). Another less conclusive argu- 
ment is, that all impressions have their effect, and the per- 
ceptible must be composed of imperceptible parts [G. V. 24, 
105, 107 (N. E. 25, 116, 118)] ; whence it is supposed to follow 
that finite perceptions, like their objects, must be infinitely 
divisible, and therefore composed of parts of which we are not 
conscious. Leibniz, in fact, identified four apparently different 
things, namely (1) unconscious perception, (2) confused per- 
ception, (.3) minute perception, and (4) psychical disposition. 
Of these four, the first is proved by the endless regress re- 
sulting from self-consciousness, and is required for maintaining 
that we always think and always mirror the whole universe. 
The second is required for explaining sense-perception, and, 
as we have seen, for the differences between different monads. 
The third follows from the argument that a perception, which 
is supposed finite, has as many parts as its object, and since 
its object may be the whole universe, the number of its parts 
may be infinite. The fourth is required to explain the sense 
in which truths are innate — a sense, by the way, very like 
that in which Kant's d priori is in the mind. All four appear 
to have been equally denied by Locke and asserted by Leibniz. 
It is worth while, therefore, to enquire into their connections. 

97. It seems evident that unconscious perception is the 
most fundamental, and that the others follow if this be ad- 
mitted. A confused perception, we may say, is such that we 
are not separately conscious of all its parts. Knowledge is 
confused, in Leibniz's phraseology, when I cannot enumerate 
separately the marks required to distinguish the thing known 
from other things (G. IV. 422 ; D. 27). And so, in confused 
perception, though I may be conscious of some elements of my 
perception, I am not conscious of all (e.g. G. V. 109 ; N. E. 120) ; 
for the perception is supposed to be as complex as its object, 
and therefore, if I were conscious of all the elements in my per- 
ception, I could wholly distinguish the object from other different 
objects. The parts which I do not distinguish are minuted 

' Cf. G. IV. 574: "At bottom confused thoughts are nothing but a multitude 
of thoughts which in themselves are like those that are distinct, but are so small 
that each separately does not excite our attention, and does not cause us to 
distinguish it." 



158 CONFUSED AND UNCONSCIOUS PERCEPTION. 

Again, as regards minute perceptions, Leibniz holds, with 
modern psycophysics, that a perception must reach a certain 
magnitude before we become aware of it, and thus sufficiently 
minute perceptions are necessarily unconscious. Psychical 
dispositions, finally, are a name for something which must 
be assumed by anyone who holds that every mind has a 
definite nature, and is not Locke's tabula rasa ; but the 
name per se is not an explanation, which Leibniz's theory is 
intended to be. Locke had denied that any truth is innate, 
because whatever we know has been learnt. Leibniz, in reply, 
does not, like Shelley on Magdalen Bridge, show astonish- 
ment that babies should forget so soon. But he says that 
innate truths are always in the mind, but are only elicited, 
i.e. made objects of apperception, by experience and education. 
The senses, he says, give the material for reflection ; we 
should not think of thought, if we did not think of some- 
thing else, i.e. of the particular things which the senses 
furnish (G. v. 197 ; N. E. 220). There may, he confesses, be 
innate truth? in the soul, which the soul never knows ; but 
until it knows them, it cannot know they were always there 
(G. V. 75 ; N. E. 80). That is to say, the mind perceives these 
truths, but is not conscious of perceiving them. This is an 
explanation of the vague idea of psychical dispositions by 
means of unconscious perception. Leibniz explains that when 
he says truths are innate, he does not mean simply that the 
mind has the faculty of knowing them, but that it has the 
faculty of finding them in itself (G. v. 70 ; N. E. 74— 5)^. 
Everything we know is developed out of our own nature, that 
is, it is obtained by reflection, by rendering conscious the 
perceptions which before were unconscious. Thus all in the 
end depends upon unconscious perception, whose possibility 
was denied by Locke, and whose necessity was demonstrated by 
Leibniz. 

At the same time, it would appear that minute and un- 
conscious perceptions are, after all, very nearly synonymous, 
and that confused perceptions are such as contain parts which 

^ It cannot be denied, however, that both in the remainder of this passage, 
and elsewhere, he falls back into the explanation of truths as psychical disposi- 
tions [e.g. G. V. 79, 97 (N. E. 84, 105)]. 



CONFUSED AND UNCONSCIOUS PERCEPTION. 159 

are minute or unconscious. To begin with, not all cognitions 
are confused. The knowledge of a necessary truth is distinct 
and indivisible — if we have it at all, it is not confused. And 
in any given complex perception, if any part be distinctly 
known, that part may be separated from the remainder, which 
alone is properly confused. Since our perceptions are always 
partially correct, the part which is correct may be abstracted 
as distinct perception, and only the remainder will be confused. 
For example, in the perception of matter, since there really 
is plurality, it is not in the plurality that our conception is 
confused. The confusion lies in the apparent continuity of 
parts, and this is due to their minuteness. And in all Leibniz's 
favourite illustrations of confused perception — e.g. the roar 
of the sea, which is composed of noises made by separate 
waves — he always insists on the minuteness of the constituents. 
Thus it seems that we may identify minute and unconscious 
perception. This, however, would create a difficulty in the 
explanation of innate truths of which we are unconscious, un- 
less we suppose that our perception of such truths may grow 
intensively greater and less, without being divisible into parts. 
On this point there is, to my knowledge, nothing definite in 
Leibniz. He does not seem to have perceived that confused 
perception, if it gives any true knowledge, must be partly 
distinct; and this, I think, prevented him from a clear per- 
ception of the relation between confusion and minuteness. 
The use which he made of these will appear further in the 
next chapter, where we shall have to examine his theory of 
knowledge. 



160 



CHAPTER XIV. 

LE[BNIZ'S THEORY OF KNOWLEDGE. 

98. Before I begin an account of Leibniz's theory of 
knowledge, I may as well point out that what I am going to 
discuss is not exactly Epistertiology, but a subject which 
belongs in the main to Psychology. The logical discussions of 
Chapters II. — V. dealt with that part, in what is commonly 
called Epistemology, which seems to me not psychological. 
The problem we are now concerned with is of a different kind ; 
it is not the problem : What are the general conditions of 
truth ? or. What is the nature of propositions ? It is the 
entirely subsequent problem, How do we and other people 
come to know any truth ? What is the origin of cognitions as 
events in time ? And this question evidently belongs mainly 
to Psychology, and, as Leibniz says, is not preliminary in 
philosophy [G. v. 15 (N. E. 15; D. 95)]. The two questions 
have been confused — at any rate since Des Cartes — because » 
people have supposed that truth would not be true if no one 
knew it, but becomes true by being known. Leibniz, as we 
shall see in discussing God, made this confusion, and Locke 
might seem to have made it, since he disclaims a merely 
psychological purposed But that is no reason for onr making 
it, and in what follows I shall try to avoid it. At the same 
time Locke is in one sense justified. The problem is not a 
purely psychological one, since it discusses knowledge rather 
than belief From the strict standpoint of Psychology, no 
distinction can be made between true and false belief, between 
knowledge and error. As a psychical phenomenon, a belief 
1 Essay, Introduction, § 2. 



Leibniz's theory of knowledge. 161 

may be distinguished by its content, but not by the truth or 
falsity of that content. Thus in discussing knowledge, i.e. the 
belief in a true proposition, we presuppose both truth and 
belief. The inquiry is thus hybrid, and subsequent both to the 
philosophical discussion of truth, and to the psychological 
discussion of belief 

99. I explained briefly in my last chapter the sense in 
which Leibniz held to innate ideas and truths. They are in 
the mind always, but only become properly known by b e- 
c oming conscious objects of apperception. Leibniz only 
endeavours, in the New Essays^to^ show "the innateness of 
necessary truths, though he is bound to hold, owing to the 
independence of monads, that all the truths that ever come to 
be known are innate. He finds it easier, however, to prove 
the impossibility of learning necessary truths by experience, 
and trusis, I suppose, that this will afford a presumption 
against Locke's whole theory of knowledge. He uses the 
expression innate truth in the New Essays, to denote a truth 
in which all the ideas are innate, i.e. not derived from sense ; 
but he explains that there is a different use of the word 
[G. V. 66 (N. E. 70)]. fin the sense in which he uses it, " the 
sweet is not the bitter " is not innate, because sweet and 
bitter come from the external senses. But " the square is not 
the circle " is innate, because squgxe and circle are ideas 
furnished by the understanding itselfJG. V. 79 (N. E. 84)]. 
Now the question arises : How does Leibniz distinguish ideas 
of sense from other ideas ? For he cannot hold, as other 
philosophers might, that ideas of sense are impressed from 
without. Nor can he hold that they are such as alone are 
capable of representing external things, for they are one and all 
confused, and would be absent in a true knowledge of the 
world [G. V. 77, 109 (N. E. 82, 120)].rSgnse-ideas must, there- 
fore, be distinguished by their own nature, and not by a 
reference to external causesM On this point, Leibniz, so far 
as I know, says nothing quite definite. The nearest approach 
to a definite explanation is in the Discours de Metaphysique 
(G. IV. 452). He speak.'s of the a.p.tinn nf obj ects of sen se 
u pon us. he says, in the same way as a Cpperninan — may 
speak of sunrise. There is a sense in which substances may 
E. L. H 



162 Leibniz's theory of knowledge. 

be said_tfl_act jnpop e a ch othe r, " and in this same sense it may 
be said that we receive knowledge from without, by the minis- 
tration of the senses, because some external things contain or 
express more particularly the reasons which determine our soul 
to certain thoughts." [Thus sense-ideas are those in which we 
are passive in the sense explained in Chapter XII. Again 
sense-ideas are confused and express the external world. "Dis- 
tinct ideas are a representation of God, confused ideas are a 
representation of the universe" [G. v. 99 (N. E. 109)]. He 
does, as a matter of fact, denote as sense-ideas all those which 
presuppose extension OTgpatial externality, though space itself 
is not an idea of sense. \ "The ideas which are said to. come from 
more than one sense," ne explains, " like those of space, figure, 
motion, rest, are rather from common-sense, that is from the 
mind itself, for they are ideas of the pure understanding, 
but they are related to the external, and the senses make 
us perceive themJj[G. v. 116 (N. E. 129)]. S^hus the quali- 
ties which appear as external are ideas of sense, but all that 
is involved in externality itself is not sensationaO And the 
qualities that appear as external are confuse^since they 
cannot, as they appear, be states of monads. \Ideas derived 
from reflection, on the contrary, are not necessarily confused 
(cf G. II. 265), for if they truly describe our own states of 
mind, they describe something actual and not a mere phe- 
nomenon. Besides this reason, there is also the fact that by 

r reflection we discover the categories (or predicaments, as 
Leibniz calls them). There is, indeed, much that reminds 
one of Kant in Leibniz's theory of knowledge. \Existence, he 
says, cannot be found in sensible objects but by the aid of 
reason, and hence the idea of existence is derived from re- 
flecti^[G. V. 117 (N. E. 130)]. (To the maxim that there is 
nothing in the intellect but what comes from the senses, 
Lmhniz adds, except the intellect itself (G. v. 100; N. E. 111). 

\_" It is very true," he says, " that our perceptions of ideas come 
either from the external senses, or from the internal sense, 
which may be called reflection; but this reflection is not 
limited to the mere operations of the mind, as is stated (by 
Locke); it extends even to the mind itself, ^d it is in per- 
ceiving the mind that we perceive substance " Vg. v. 23 (N. E. 



LEIBNIZ S THEORY OF KNOWLEDGE. 

24)]. The soul, he says, is innate to itself, and therefore coi 
tains certain ideas essentially [G. III. 479 ; G. v. 93 (N. E. 100)1, 
Thus it comprises being, unity, substance, identity, cause, 
perception, reason, and many other notions which the senses 
cannot give [G. v. 100 (N. E. Ill)] ; and these ideas are pre- 
supposed in any knowledge that can be derived from the 
senses. And necessary truths, Leibniz points out, are certainly 
known, though the senses cannot show them to be necessary 
[G. V. 77 (N. E. 81)]. It follows that such truths are developed 
from the nature of the mind. It may be surmised that Leibniz 
dwelt on necessary truths because, in their case, knowledge 
cannot be supposed due to a causal action of what is known 
upon the mind. For what is known, in this case, is not in time, 
and therefore cannot be the cause of our knowledge. This 
made it easier to suppose that knowledge is never caused by 
what is known, but arises independently from the nature of the 
mind. 

100. The doctrine of innate truths, as developed in the 
New Essays, is more like Kant's doctrine than it has any right 
to be. Space and time and the categories are innate, while the 
qualities which appear in space are not innate. To the general 
theory that all truths which are known are innate, which 
Leibniz should have adopted, there is no answer but one which 
attacks the whole doctrine of monads. But to the theory of 
the New Essays, which adopts the common-sense view that 
sense-perceptions are caused by their objects, while innate 
truths are incapable of such a cause, there are, I think, answers 
which apply equally against Kant's doctrine that the d priori 
is subjective. The argument for subjectivity seems to be 
simply this : When what we know is the existence of something 
now, our knowledge may be supposed caused by that existence, 
since there is a temporal relation between them. But when 
what we know is an eternal truth, there can be no such 
temporal relation. Hence the knowledge is not caused by what 
is known. But nothing else, it is held, could have caused it 
unless the knowledge had been already obscurely in the mind. 
Hence such knowledge must be, in some sense, innate. It is 
difficult to state this argument in a form which shall be at all 
convincing. It seems to depend upon the radically vicious 

11—2 



164 LEIBNIZ'S THEORY OF KNOWLEDGE. 

disjunction that knowledge must be either caused by what is 
known or wholly uncaused. In Leibniz, who rejected a causal 
action of the objects of perception, this argument, as a means 
of distinguishing different kinds of knowledge, is peculiarly 
scandalous. But leaving aside this special doctrine, and 
admitting that objects cause our perceptions, does it follow that 
necessary truths must be innate ? All who hold this view are 
compelled, like Leibniz, to admit that innate knowledge is only 
virtual [G. V. 71 (N. E. 76)], while all conscious knowledge is 
acquired, and has its definite causes. Now if the knowledge 
can be rendered conscious by causes other than what is known, 
why cannot it be wholly due to such causes ? All that we can 
say is, that the mind must have had a disposition towards such 
knowledge — a vague phrase which explains nothing. Moreover, 
the same argument applies to sense-perception. If the mind 
were not capable of sense-knowledge, objects could not cause 
such knowledge. Sensations of colours, sounds, smells, etc., must 
be equally innate on this view. There is, in fact, just the same 
difficulty in admitting conscious knowledge of a necessary truth 
to be caused, as in admitting any knowledge of it to be caused. 
The difficulty, in each case, is manufactured by supposing that 
knowledge can only be caused by what is known. This sup- 
position wcjuld have disappeared if people had asked themselves 
what really is known. It is supposed that in cb priori know- 
ledge we know a proposition, while in perception we know an 
existent. This is false. We know a proposition equally in 
both cases. In perception we know the proposition that some- 
thing exists, It is evident that we do not merely know the 
something, whatever it be, for this is equally present in mere 
imagination. What distinguishes perception is the knowledge 
that the something exists. And indeed whatever can be known 
must be true, and must therefore be a proposition. Perception, 
we may say, is the knowledge of an existential proposition, not 
consciously inferred from any other proposition, and referring to 
the same or nearly the same time as that in which the know- 
ledge exists. If this had been duly realized — if people had 
reflected that what is known is always a proposition — they would 
have been less ready to suppose that knowledge could be caused 
by what is known. To say knowledge is caused in perception 



Leibniz's theory of knowledge. 165 

by what exists, not by the fact that it exists, is at once to admit 
that such knowledge is not caused by what is known. Thus 
perception and intellectual knowledge become much more akin 
than is generally supposed. We must either hold all knowledge 
to be always in the mind, in which case its emergence into 
consciousness becomes a problem, or we must admit that all 
knowledge is acquired, but is never caused by the proposition 
which is known. What its causes are, in any particular case, 
becomes a purely empirical problem, which may be left wholly 
to Psychology. 

101. There is, moreover, a great diflSculty as to what 
Leibniz meant by ideas which are innate. This question is 
dealt with in the New Essays, at the beginning of Book II 
[G. V. 99 (N. E. 109)]. " Is it not true," Locke is made to ask, 
"that the idea is the object of thought?" "I admit it," 
Leibniz replies, " provided you add that it is an immediate 
internal object, and that this object is an expression of the 
nature or the qualities of things. If the idea were the form 
of thought, it would spring up and cease with the actual 
thoughts which correspond to it ; but being the object, it may 
be before and after the thoughts'." Thus an idea, though it 
is in the mind, is neither knowledge nor desire; it is not a 
thought, but what a thought thinks about. This passage 
makes it clear that the only reason Leibniz had for saying ideas 
exist in the mind is that they evidently do not exist outside of 
it. He seems never to have asked himself why they should be 
supposed to exist at all, nor to have considered the difficulty in 
making them merely mental existents. Consider, for example, 
the idea 2. This is not, Leibniz confesses, my thought of 2, 
but something which my thought is about. But this some- 
thing exists in my mind, and is therefore not the same as the 
2 which some one else thinks of Hence we cannot say that 
there is one definite number 2, which different people think of; 
there are as many numbers 2 as there are minds. These, it 
will be said, all have something in common. But this some- 
thing can be nothing but another idea which will, therefore, in 
turn, consist of as many different ideas as there are minds. 
Thus we are led to an endless regress. Not only can no two 
1 Of. also G. III. 659 (D. 236) ; iv. 451. 



166 LEIBNIZ'S THEORY OF KNOWLEDGE. 

people think of the same idea, but they cannot even think of 
ideas that have anything in common, unless there are ideas 
which are not essentially constituents of any mind. With 
Locke's definition, that an idea is the object of thouglit, we may 
agree ; but we must not seek to evade the consequence that an 
idea is not merely something in the mind, nor must we seek to 
give every idea an existence somewhere else. Precisely the 
same criticism applies to the statement that knowledge, ideas 
and truths "are only natural habits, i.e. active and passive 
dispositions and aptitudes" (N. E. 105 ; G. v. 97). 

102. Sense-knowledge in Leibniz is not properly dis- 
tinguished from intellectual knowledge by its genesis, but by its 
nature. It differs in that the qualities with which it deals are 
spatially extended, and are, one and all confused. From their 
confusion it follows that those which seem simple are in reality 
complex, though we are unable to make the analysis. Thus 
green, though it appears simple, is, Leibniz thinks, really a 
mixture of insensible portions of blue and yellow [G. v. 275 
(N. E. 320)]. But how blue and yellow would appear, if they 
were distinctly perceived, he does not inform us. He seems to 
think, however, as was natural to one who believed in analytic 
judgments, that the nature of our evidence for necessary and for 
sensational truths is different. The first truth of reason, he 
says, is the law of contradiction, whilst the first truths of fact 
are as many as the immediate perceptions. That I think is 
no more immediate than that various things are thought by 
me, and this is iirged as a criticism of Des Cartes' cogito 
[G. IV. 357 (D. 48)]. That is' to say, the law of contradiction 
is the sole ultimate premiss for necessary truths, but for con- 
tingent truths there are as many ultimate premisses as there 
are experiences. Nothing, he says, should be taken as primitive 
principles, except experiences and the law of identity or contra- 
diction, without which last there would be no difference be- 
tween truth and falsehood [G. v. 14 (D. 94 ; N. E. 13)]. Thus 
many truths of fact have no evidence except self-evidence, but 
this is only the case, among necessary truths, as regards the 
law of contradiction. The self-evident truths of fact, however, 
are all psychological : they concern our own thoughts. To this 
extent Leibniz is at one with Des Cartes and with Berkeley. 



LEIBNIZ'S THEORY OF KNOWLEDGE. 167 

Where he is more philosophical than either is in perceiving 
that truths of fact presuppose necessary truths, and that our 
own existence is not therefore an ultimate and fundamental 
premiss for all truths. My own existence is an axiom, he says, 
in the sense of being indemonstrable, not in the sense of 
being necessary [G. v. 391 (N. E. 469)]. Like all finite exist- 
ence, it is contingent, but it is just as certain as necessary 
truths (N. E. 499; G. v. 415). Thus Leibniz agrees with Locke 
that we have an intuitive knowledge of our own existence, a 
demonstrative knowledge of God's existence, and a sensitive 
knowledge of that of other things (ib.). But the sensitive 
knowledge may be doubted, and cannot be accepted without 
some general ground for the existence of other things [G. V. 117 
(N. E. 130)]. In this theory which, in its general outlines, is 
more or less Cartesian, there are, as I have already pointed out, 
two distinct advances upon Des Cartes. The first is that my 
own existence is not taken as the premiss for necessary truths ; 
the second is that the existence of my various thoughts is as 
certain as the existence of myself Leibniz did not discover, 
what seems equally true, that the existence of external things 
is just as certain and immediate as that of my own thoughts, 
and thus he was unable, as we saw, to justify his belief in 
an external world. 

103. I come now to another respect in which Leibniz 
refined upon Des Cartes, namely in the doctrine known as the 
quality of ideas. This is developed in the " Thoughts on 
Knowledge, Truth and Ideas" (D. 27—32; G. iv. 422—6) 
(1684). Des Cartes held that whatever is clearly and dis- 
tinctly conceived is true. This maxim, Leibniz points out, 
is useless without criteria of clearness and distinctness [G. iv. 
425 (D. 31)]. He therefore lays down the following defini- 
tions. Knowledge is either obscure or clear. Clear knowledge 
is confused or distinct. Distinct knowledge is adequate or 
inadequate, and is also either symbolical or intuitive. Perfect 
knowledge is both adequate and intuitive. 

As to the meanings of these terms, a notion is obscure when 
it does not enable me to recognize the thing represented, or 
distinguish it from other similar things ; it is clear when it does 
enable me to recognize the thing represented. Clear knowledge 



168 Leibniz's theory of knowledge. 

is confused when I cannot enumerate separately the marks 
required to distinguish the thing known from other things, 
although there are such marks. Instances of this are colours 
and smells, which though we cannot analyze them, are certainly 
complex, as may be seen by considering their causes. (We 
must remember that Leibniz believed perception to have 
always the same degree of complexity as its object, and since 
green can be produced by mixing blue and yellow, a green 
object is complex, and therefore our perception of green is also 
complex.) Clear knowledge is distinct, either when we can 
separately enumerate the marks of what is known — i.e. when 
there is a nominal definition — or where what is known is 
indefinable but primitive, i.e. an ultimate simple notion. Thus 
a composite notion, such as gold, is distinct when all its marks 
are known clearly ; it is adequate, if all the marks are also 
known distinctly ; if they are not known distinctly, the know- 
ledge is inadequate. Leibniz is not certain whether there is 
any perfect example of adequate knowledge, but Arithmetic, 
he thinks, approaches it very nearly. Distinct knowledge is 
also divided according as it is symbolical or intuitive. It is 
symbolical or blind, when we do not perceive the whole nature 
of the object at one time, but substitute signs or symbols, as in 
Mathematics, whose meaning we can recall when we will. 
When we embrace in thought at once all the elementary 
notions which compose an idea, our thought is intuitive. Thus 
our knowledge of distinct primitive ideas, if we have it, must be 
intuitive, while our knowledge of complex notions is, in general, 
only symbolical. 

104. This doctrine has important bearings on definition. 
A real definition, as opposed to one which is merely nominal, 
shows the possibility of the thing defined, and though this may 
be done d posteriori, by showing the thing actually existing, it 
may also be done cb priori, wherever our knowledge is 
adequate. For in this case, a complete analysis has been 
effected without discovering any contradiction ; and where 
there is no contradiction, that which is defined is necessarily 
possible [G. iv. 424 — 5 (D. 30)]. On definition generally, 
Leibniz makes many important observations. A definition is 
only the distinct exposition of an idea [G. V. 92 (N. E. 99)], 



LEIBNIZ'S THEORY OF KNOWLEDGE. 169 

but it may be either real or nominal. It is nominal when 
it merely enumerates marks, without showing them to be 
compatible. It is real when all the marks are shown to be 
compatible, so that what is defined is possible. The idea 
defined is then real, even if nothing ever exists of which it 
can be predicated [G. v. 279 (N. E. 325)]. Simple terms can- 
not have a nominal definition ; but when they are only simple 
with regard to us, like green, they can have a real definition 
explaining their cause, as when We say green is a mixture of 
blue and yellow [G. v. 275 (N. E. 319)]. The continuity of 
forms gives him some trouble in regard to definition, and com- 
pels him to admit that we may be in doubt whether some 
babies are human or not. But he points out, against Locke, 
that though we may be unable to decide the question, there 
always is only one true answer. If the creature is rational, it 
is human, otherwise it is not human ; and it always is either 
rational or not rational, though we may be in doubt as to 
the alternative to be chosen [G. v. 290 (N. E. p. 339)]. There 
is, however, a real difficulty in all cases of continuity, that 
an infinitesimal change in the object may make a finite change 
in the idea; as the loss of one more hair may just make a 
man bald. In such cases, Leibniz thinks that nature has not 
precisely determined the notion [G. V. 281 (N. E. 328)] ; but 
this seems an inadequate reply. 

105. Connected with Leibniz's notion of definitions, and 
of the reduction of all axioms to such as are identical, or 
immediate consequences of definitions [G. V. 92 (N. E. 99)], 
is his idea of a Characteristica Universalis, or Universal 
Mathematics. This was an idea which he cherished through- 
out his life, and on which he already wrote at the age of 
20'. He seems to have thought that the symbolic method, 
in which formal rules obviate the necessity of thinking, could 
jH-oduce everywhere the same fruitful results as it has produced 
in the sciences of number and quantity. " Telescopes and 
microscopes," he says, " have not been so useful to the eye 
as this instrument would be in adding to the capacity of 
thought " (G. VII. 14). " If we had it, we should be able to 
reason in metaphysics and morals in much the same way as 
' In the Dissertatio de Arte Combinatoria, G. it. 27 — 102. 



170 Leibniz's theory of knowledge. 

in geometry and analysis " (G. viL 21). " If controversies 
were to arise, there would be no more need of disputation 
between two philosophers than between two accountants. 
For it would suffice to take their pencils in their hands, to sit 
down to their slates, and to say to each other (with a friend 
as witness, if they liked) : Let us calculate '' (G. vii. 200). 
By establishing the premisses in any ct priori science, the 
rest, he thought, could be effected by mere rules of inference ; 
and to establish the right premisses, it was only necessary 
to analyze all the notions employed until simple notions were 
reached, when all the axioms would at once follow as identical 
propositions. He urged that this method should be employed 
in regard to Euclid's axioms, which he held to be capable of 
proof [G. V. 92 (N. E. 99)]. The Universal Characteristic seems 
to have been something very like the syllogism. The syllogism, 
he says, is one of the most fruitful of human inventions, a kind 
of universal Mathematics [G. V. 460 (N. E. 559)]. What he 
desired was evidently akin to the modern science of Symbolic 
Logic', which is definitely a branch of Mathematics, and was 
developed by Boole under the impression that he was deal- 
ing with the " Laws of Thought." As a mathematical idea — 
as a Universal Algebra, embracing Formal Logic, ordinary 
Algebra, and Geometry as special cases — Leibniz's conception 
has shown itself in the highest degree useful. But as a 
method of pursuing philosophy, it had the formalist defect 
which results from a belief in analytic propositions, and which 
led Spinoza to employ a geometrical method. For the business 
of philosophy is just the discovery of those simple notions, 
and those primitive axioms, upon which any calculus or 
science must be based. The belief that the primitive axioms 
are identical leads to an emphasis on results, rather than 
premisses, which is radically opposed to the true philosophic 
method. There can be neither difficulty nor interest in the 
premisses, if these are of such a kind as " A is A " or " AB 
is not non-A." And thus Leibniz supposed that the great 
requisite was a convenient method of deduction. Whereas, 



> Cf. G. vn. 214—15, 230, where several of the rules of the Calculus of 
Symbolic Logic are given. 



LEIBNIZ'S THEORY OF KNOWLEDGE. l7l 

in fact, the problems of philosophy should be anterior to 
deduction. An idea which can be defined, or a proposition 
which can be proved, is of only subordinate philosophical 
interest. The emphasis should be laid on the indefinable and 
indemonstrable, aad here no method is available save intuition. 
The Universal Characteristic, therefore, though in Mathematics 
it was an idea of the highest importance, showed, in philo- 
sophy, a radical misconception, encouraged by the syllogism, 
and based upon the belief in the analytic nature of neces- 
sary truths \ 



1 For an account of Leibniz's views on this matter see Guhrauer, op. cit. 
Vol. I. p. 320 ff. For a full treatment, see Couturat, La Logique de Leibnitz, 
Paris, 1900 (in the press). 



172 



CHAPTER XV. 



PROOFS OF THE EXISTENCE OF GOD. 

106. I COME uow to the weakest part in Leibniz's phi- 
losophy, the part most full of inconsistencies. Whatever, in 
the doctrine we have examined, seemed arbitrary, or in need 
of further explanation, was easily explained by the lazy device 
of reference to an Omnipotent Creator. And not only unavoid- 
able difficulties, but others which might have been avoided, 
were left, because they reinforced the arguments upon which 
Leibniz's orthodoxy loved to dwell. A philosophy of substance, 
we may say generally, should be either a monism or a monad- 
ism. A monism is necessarily pantheistic, and a monadism, 
when it is logical, is as necessarily atheistic. Leibniz, how- 
ever, felt any philosophy to be worthless which did not estab- 
lish the existence of God, and it cannot be denied that certain 
gaps in his system were patched up by a reference to the 
Divine Power, Goodness and Wisdom. Let us now examine 
what the arguments were by which this result was attained. 

There are four distinct arguments, in Leibniz, which 
attempt to prove the existence of God. Only one of these, so 
far as I know, was invented by him, and that was the worst of 
the four. They are : The Ontological Argument, the Cosmo- 
logical Argument, the Argument from the Eternal Truths, and 
the Argument from the Pre-established Harmony. 

107. The Ontological Argument, which Des Cartes had 
adapted from Anselm, is not much used by Leibniz, and is, in 
the Cartesian form, severely criticized by him. At the same 
time, it and the argument from the eternal truths alone start 



PROOFS OF THE EXISTENCE OF GOD. 173 

from necessary premisses, and alone, therefore, are formally 
capable of bringing out a necessary result. And it is, of 
course, quite essential to show that God's existence is a neces- 
sary truth. Moreover, if this be true, the Ontological Argu- 
ment must be substantially correct. For if it is self-contra- 
dictory to suppose that God does not exist, it follows that his 
existence is of his essence, and consequently, that his existence 
can be inferred from his essence. And this is precisely what 
the Ontological Argument attempts. Accordingly Leibniz is 
careful not wholly to reject it. 

The Ontological Argument rnay be put in many ways. In 
its original form, it states that God has all perfections, and 
existence is among perfections — that is, the good is better if it 
exists than if it does not exist. Consequently existence is of 
God's essence ; to suppose that the most perfect Being does not 
exist, is self-contradictory. Again God may be defined, without 
reference to the Good, as the most real Being, or the sum of all 
reality, and then equally it follows from his essence that he 
exists. To these arguments Leibniz objected that they do not 
prove the idea of God to be a possible idea. They prove, he 
admits, what is true only of God, that if he be possible he 
exists [e.g. G. v. 419 (N. E. 504) ; G. vi. 614 (D. 224 ; L. 242)]. 
This objection had been already made to Des Cartes, and 
replied to in the answers to the second objections to his Medi- 
tations'. Leibniz showed, without difficulty, that the idea of 
God is possible. His possibility follows a posteriori from the 
existence of contingent things ; for necessary being is being of 
itself, and if this were not possible, no being would be possible 
[G. IV. 406 (D. 137)]. But this line of argument belongs 
rather to the cosmological proof. God's possibility follows 
a priori from his having no limitations, no negation, and there- 
fore no contradiction [G. VI. 614 (D. 224; L. 242)]. This 
argument is well stated in the paper which Leibniz submitted 
to Spinoza at the Hague in 1676, with the title, "That the 
most perfect Being exists"." The contents of this paper, in 
spite of its early date, are in complete harmony with his later 

' See Oeuvres de Des Cartes, ed. Cousin, Vol. i. pp. 407, 440 ff. 
2 G. vn. 261 (N. E. 714). Also Stein, Leibniz u. Spinoza, Beilage i. Of. 
Beilage vii., Jan. 1678. 



174 PROOFS OF THE EXISTENCE OF GOD. 

philosophy. He undertakes to prove, from premisses which 
he always accepted, that God is possible, and then uses the 
Ontological Argument to show that God is actual. Thus he 
prefaces the Ontological Argument by exactly the reasoning 
which he always held to be required. 

108. The argument is as follows. Every quality which is 
simple or absolute, positive and indefinable, and expresses its 
object without limits, is a perfection. All such qualities can be 
predicates of one and the same subject. For let us assume that 
two of them, A and B, are incompatible. Their incompatibility, 
Leibniz says, cannot be proved without resolving them, other- 
wise their nature would not enter into the reasoning. But 
both are irresolvable. Nor can their incompatibility, Leibniz 
thinks, be known per se. Hence, A and B are not incompatible, 
and such a subject is possible. And since existence is a per- 
fection, such a subject exists. 

This reasoning is certainly valid, in so far as it proves that 
God, so defined, is not self-contradictory ; and with the analytic 
theory of necessary judgments, this is all that is required to 
prove him possible. The interesting point, however, is the 
Ontological Argument itself, which is involved in saying that 
since existence is a perfection, God exists. This depends upon 
regarding existence as a predicate, which Leibniz does [G. v. 
339 (N. E. 401)]. But he recognizes, as regards finite things, 
a great difference between existence and ail other predicates. 
Existential judgments alone are not analytic. In any proposi- 
tion in which the predicate is not existence, the predicate is 
contained in the subject ; but when the predicate is existence, 
it is not so contained, except in the one case of God. Leibniz 
would have admitted, what Kant urged, that a hundred thalers 
which I merely imagine are exactly like a hundred thalers 
which really exist ; for this is involved in the synthetic nature 
of assertions of existence. If this were not the case, the notion 
of a hundred actual thalers would be different from that of a 
hundred possible thalers ; existence would be contained in the 
notion, and the existential judgment would be analytic. But 
Leibniz ought not to have held existence to be a predicate at 
all, since two subjects, one of which has a given predicate, 
while the other does not have it, cannot possibly be exactly 



PROOFS OF THE EXISTENCE OF GOD. 175 

alike. He ought, therefore, to have arrived at Kant's position, 
that existence is not a predicate, and that God's non-existence 
cannot be self-contradictory'. , He endeavoured, instead, to 
bridge the gulf between contingent and necessary truths, i.e. 
between such as are existential and such as are not so, by 
means of the necessary existence of God. This attempt is at 
the bottom of all his arguments, and is especially obvious in the 
case of the cosmological argument, which we must now examine. 
109. The cosmological argument is, at first sight, more 
plausible than the ontological argument, but it is less philo- 
sophical, and derives its superior plausibility only from conceal- 
ing its implications. It has a formal vice, in that it starts from 
finite existence as its datum, and admitting this to be con- 
tingent, it proceeds to infer an existent which is not contingent. 
But as the premiss is contingent, the conclusion also must be 
contingent. This is only to be avoided by pointing out that 
the argument is analytic, that it proceeds from a complex 
proposition to one which is logically presupposed in it, and that 
necessary truths may be involved in those that are contingent. 
But such a procedure is not properly a proof of the presupposi- 
tion. If a judgment A presupposes another B, then, no doubt, 
if A is true, B is true. But it is impossible that there should 
be valid grounds for admitting A, which are not also grounds 
for admitting B. In Euclid, for example, if you admit the 
propositions, you must admit the axioms; but it would be 
absurd to give this as a reason for admitting the axioms. Such 
an argument is at best ad hominem, when your opponent is a 
poor reasoner. If people are willing to admit finite existence, 
then you force them to admit God's existence ; but if they ask 
a reason why they should admit finite existence, the only 
grounds, if the cosmological argument be valid, are such as 
lead first to the existence of God; such grounds, however, if 
they exist, are only to be found in the ontological argument; 
and this Leibniz virtually admits by calling this proof an argu- 
ment dk posteriori [G. vi. 614 (D. 224; L. 242)]. 

1 "Being is evidently not a real predicate, i.e. a conception of something, 
which could be added to the conception of a thing. It is merely the positing of 
a thing, or of certain determinations, in itself" (Eeine Vemunft, ed. Hart, 
p. 409). 



176 PROOFS OF THE EXISTENCE OF GOD. 

The cosmological argument, as Leibniz states it, is briefly 
as follows. The present world is necessary hypothetically, but 
not absolutely. Since it is what it is, it follows that it will be 
what it will be. But causality, which connects one state of the 
world with the next, never shows why there is any world at 
all. Even if we suppose the eternity of the world, we cannot 
escape the necessity for some reason of the whole series ; 
though each state follows from the preceding, we never get a 
sufficient reason why there are any states at all. Hence there 
must be some extramiindane reason of things. The whole 
collection of finite existents is contingent, and therefore 
demands a sufficient reason ; but this cannot be found within 
the series, since every term is contingent, and itself requires a 
sufficient reason. Hence the sufficient reason of all contingents 
must be itself not contingent, but metaphysically necessary. 
Moreover the reason of the existing can only be derived from 
the existing. Hence the metaphysically necessary sufficient 
reason of all contingents must be a necessary existent, i.e. a 
Being whose essence involves existence ; and this can only be 
God [G. VII. 302 (D. 100; L. 337)]. 

110. This argument is open to attack on the ground that, 
if the reason of an existent can only be some other existent, 
then the ontological argument cannot be valid. "For in 
eternal things it must be understood that, even if there were 
no cause, there is a reason, which, in perduring things, is 
necessity itself or essence " {Ih.). Thus it is only the reason 
of a contingent existent that must be an existent. But this 
can only be on the ground that the reason of the contingent 
must be one that inclines, but does not necessitate, which is, 
indeed, of the very essence of contingency. Accordingly, when 
God's necessary existence has been obtained, the world of con- 
tingents must not follow -from it necessarily. It follows that 
God's volitions must be contingent, for they necessarily attain 
their effects, and if these effects are to be contingent it can 
only be, therefore, because the volitions are contingent. The 
volitions themselves, therefore, require a sufficient reason, 
which inclines but does not necessitate. This is found in God's 
goodness. It is held that God is free to do evil, but does not 
do so [G. VI. 386 (D. 203) ; G. vii. 409 (D. 274)]. But God's 



PROOFS OF THE EXISTENCE OF GOD. 177 

goodness itself must be supposed necessary (cf. p. 39 supra). 
Thus the contingency of existential propositions rests ulti- 
mately upon the assertion that God does not necessarily do 
good (G. IV. 438). God's good actions, in fact, have to be 
conceived as a collection of particular existents, each having a 
sufficient reason in his goodness. Or else we may place their 
sufficient reason in his wisdom, namely in his knowledge of 
the good, which is a knowledge of necessary propositions. 
God's goodness, Leibniz says, led him to desire to create the 
good, his wisdom showed him the best possible, and his power 
enabled him to create it (G. vi. 167). 

But to return to the cosmological argument. By saying 
that the whole world of contingents is still contingent, and 
must have a reason in some metaphysically necessary Being 
other than itself, Leibniz endeavours to exclude the pantheism 
which lurks in all arguments for God. He might equally well 
have said that every finite existent is conditioned by some 
other existent, but the whole series of existents cannot be con- 
ditioned by any existent. It would follow that its sufficient 
reason was not an existent, and therefore that the sum total of 
existence is metaphysically necessary. This form of argument 
would, however, have landed him in Spinozism. It is very 
analogous to the form used by Mr Bradley, and it really under- 
lies Leibniz's argument. Its validity is indisputable if the 
existential theory of judgment be admitted. To maintain that 
there is no truth is self-contradictory, for if our contention were 
itself true, there would be truth. If, then, all truth consists in 
propositions about what exists, it is self-contradictory to main- 
tain that nothing exists. Thus the existence of something is 
metaphysically necessary. This argument, which is set forth 
at length in Book I., Chaps, ii. — iv. of Mr Bradley's Logic, 
partakes of both the Ontological and Cosmological arguments. 
It also suggests Leibniz's proof firom the Eternal Truths, from 
which we shall discover the sense in which he held the existen- 
tial theory of judgments. 

111. We have seen that Leibniz held the eternal truths 
to be one and all hypothetical. They do not assert the exist- 
ence of their subjects. The possible is wider than the actual, 
and all the possible worlds can only be described by eternal 
B.L. 12 



178 PROOFS OF THE EXISTENCE OF GOD. 

truths. But this view, which seems to me thoroughly sound, 
alarms Leibniz. It may be objected, he thinks, that possibilities 
or essences prior to existence are fictions. To this he replies, 
that they are not fictions, but must be sought in the mind of 
God, along with the eternal truths. The existence of the actual 
series of things, he continues, shows his assertion to be not 
gratuitous; for the reason of the series is not to be found 
within it, but must be sought in metaphysical necessities or 
eternal truths, while at the same time the reason of a con- 
tingent existent must itself exist. Therefore the eternal truths 
must have their existence in an absolutely or metaphysically 
necessary Being, i.e. in God [G. vii. 305 (D. 103; L. 343)]. 
Thus confused ideas are those which represent the universe, 
while distinct ideas, from which necessary truths are derived, 
are a representation of God (N. E. 109 ; G. v. 99). And God's 
understanding is described as the region of the eternal truths 
(G. VI. 115 ; G. VII. 311). In God those things which otherwise 
would be imaginary are realized [G. vii. 305 (D. 103 ; L. 343)]. 
Thus relations derive their reality from the supreme reason 
(G. V. 210 ; N. E. 235), i.e. from the fact that they exist in the 
divine mind. God, according to Leibniz, sees not only indi- 
vidual monads and their various states, but also the relations 
between monads and in this consists the reality of relations \ 
Thus in the case of relations, and of eternal truths generally, 
esse is percipi. But the perception must be God's perception, 
and this, after all, has an object, though an internal one [G. vi. 
614 (D. 225; L. 243)]. Thus our knowledge of the eternal 
truths becomes a knowledge of God, since these truths are 
part of God's nature. And this is why rational spirits, which 
know eternal truths, are said to mirror not only the universe 
of creatures, but also God. 

112. This argument I can only describe as scandalous. In 
the first place it confuses God's knowledge with the truths 
which God knows — a confusion which, in other places, Leibniz 
quite clearly exposes. " Essences," he says, " can, in a certain 

way, be conceived of without God And the very essence of 

God embraces all other essences to such a degree that God 

cannot be perfectly conceived without them" (D. 175 ; F. de C. 

1 G. n. 438. Cf. also Monadology, § 43. 



PROOFS OF THE EXISTENCE OF GOD. 179 

24). And again : " It can no more be said that God and the 
things known by God are one and the same thing, than that the 
mind and the things perceived by the mind are the same" 
(D. 177; F. de C. 34). This last passage is an argument against 
Spinoza, and doubtless has only existents in view. But if truths 
can be the same as the knowledge of them, why may not this be 
so when the truths are existential ? And the former passage 
cannot be thus disposed of, since it deals explicitly with essences, 
and points out the true argument, namely that God cannot be 
conceived of without essences. Moreover, as I have already 
suggested, God's existence itself, since it is proved, has a 
ground ; and this ground cannot be identified with God's know- 
ledge of it. The eternal truths, Leibniz strongly urges, do 
not depend, as Des Cartes had held, upon God's will. For this 
there are many reasons. In the first place, God's will depends 
upon a suflScient reason, which must always be his perception 
of the good. But this can only be a motive to God's choice, if 
the good itself is independent of such choice. God could have 
no motive in deciding what was to be decreed good, unless one 
possible decree was better than another, and thus we get into 
a vicious circle'- Moreover God's existence is among eternal 
truths, and who would dare, Leibniz asks triumphantly, to 
declare that God's existence is due to his will (G. vir. 310 — 1) ? 
But who would dare, we may retort, to say that God's existence 
depends upon his understanding? Would any one maintain 
that the reason of God's existence is his knowledge of it ? If 
this were the case, proofs of the existence of God ought first to 
prove that God knows of it, and thence deduce that what he 
knows, i.e. his own existence, is true. But it must be obvious 
that his existence does not depend upon his knowledge of it. 
Nor can it be maintained that the two are identical, for his 
knowledge comprises many other propositions, and he contains, 
besides knowledge, the attributes of Goodness and Power. 
Thus his existence cannot be synonymous with his knowledge 
of it. And the same is evident, on reflection, concerning all 
other truths. Leibniz maintains that God's view is veritable, 
that what he knows is true {e.g. G. iv. 439) ; and he evidently 
regards this statement as not tautological. But if truth means 
• G. VII. 365 (D. 244), 379; iv. 344. 

12—2 



180 PROOFS OF THE EXISTENCE OF GOD. 

what God knows, the statement that God's view is veritable is 
equivalent to the statement that he knows what he knows. 
Moreover, God's existence is deduced from the Law of Contra- 
diction, to which it is therefore subsequent. Hence we cannot, 
without a vicious circle, maintain that this law is only due to 
God's knowledge of it. Again, without the law of identity or 
contradiction, as Leibniz truly says [G. V. 14 (D. 94 ; N. E. 14)], 
there would be no difference between truth and falsehood. 
Therefore, without this law, it could not be true, rather than 
false, that God exists. Hence, though God's existence may 
depend upon the law of contradiction, this law cannot in turn 
depend upon God's existence. Finally, consider the very mean- 
ing of the word proposition. Leibniz has to maintain that 
eternal truths exist in the mind of God [G. vi. 230 ; vii. 305 
(D. 103 ; L. 343)]. Thus we cannot say that God is subjected 
to eternal truths, for they form part of his very nature, to wit 
his understanding. But again Leibniz speaks of them as the 
internal object of his understanding [G. vi. 614 (D. 225 ; L. 
243)], thus suggesting by the word object, what the word 
internal is intended to deny, that the truths are something 
different from the knowledge of them. And this, if we consider, 
is obvious. For how can an eternal truth exist ? The Law of 
Contradiction, or the proposition that two and two are four, or 
the truths of Geometry — ^these, we are told, exist in the mind 
of God. But it must surely be evident, if we consider the 
matter, that these truths are wholly incapable of existence, and 
that what exists is only the knowledge of them. It can scarcely 
be maintained that in studying Euclid we are studying God's 
Psychology. If, to mend matters, we were to say that truths 
actually constitute God's understanding, and if this is what 
makes them true, then, since we must always distinguish 
between a proposition and the knowledge of it, the impious con- 
sequence follows that God can have no knowledge. Truths are 
God's states of mind, and we know these truths; but God cannot 
know them, since knowledge is distinct from what is known^. 

1 This objection is urged by Leibniz himself, in a paper written probably 
about 1680, against Des Cartes. "The God of Des Cartes," he says, "has 
neither will nor understanding, since, according to Des Cartes, he has not the 
good for the object of his will, nor the true for the object of his understanding " 
(G. IV. 299). 



PROOFS OF THE EXISTENCE OF GOD. 181 

And generally if a truth be something existing in some 
mind, then that mind, and another which knows the truth, 
cannot be aware of the same truth. If we once admit that 
there is one and only one Law of Contradiction, which is 
the same whoever knows it, then the law itself is something 
distinct from all knowledge, and cannot logically depend upon 
God's mind. Unless truth be distinct from God's knowledge, 
there is nothing for God to know. God's understanding is 
constituted by knowledge of the eternal truths, and if these in 
turn are constituted by his knowledge, there is no way for his 
knowledge to begin, and no reason why it should know the 
propositions it does know rather than other propositions. Thus 
the eternal truths must be true apart from God's knowledge, 
and cannot therefore be used to prove his existence. Leibniz 
seems, in fact, never to have made up his mind as to whether 
God's understanding is a collection of truths, or the knowledge 
of this collection. The former alternative would have led to a 
God almost exactly like Spinoza's, but would have left no place 
for God's will. The latter should have left the truth of what 
God knows independent of his knowledge, and therefore not a 
ground for inferring the existence of the knowledge or of the 
Knower. 

113. We have now seen the fallacies involved in Leibniz's 
deduction of God from the eternal truths. I wish to reinforce 
the above arguments by some general remarks on truth and 
knowledge, suggested by that proof 

It is a view commonly held that, as Leibniz puts it, the 
eternal truths would not subsist if there were no understanding, 
not even God's (G. vi. 226. Of Spinoza, Ethics, ii. 7, Schol.). 
This view has been encouraged by Kant's notion that d priori 
truths are in some way the work of the mind, and has been 
exalted by Hegelianism into a first principle. Since it is self- 
contradictory to deny all truth, it has thus become self-contra- 
dictory to deny all knowledge. And since, on this view, 
nothing can be true without being known, it has become neces- 
sary to postulate either a personal God, or a kind of pantheistic 
universal Mind from whose nature truths perpetually flow or 
emanate. What I wish to point out is, that Leibniz's proof of 
God is merely a theological form of this argument, and that 



182 PROOFS OF THE EXISTENCE OF GOD. 

everything that I urged against Leibniz applies equally against 
all who make truth dependent upon knowledge. It is to be 
remembered, in this connection, that knowledge is a complex 
conception, compounded of truth and belief. Belief, as a 
psychical phenomenon, is just the same when the proposition 
believed is false as when it is true. The first difficulty en- 
countered by the view I am discussing is, therefore, the distinc- 
tion between true and false belief, between knowledge and 
error. The second difficulty is analogous to the difficulty of 
supposing the truth that God exists to be dependent upon 
God's knowledge of this truth. Is the proposition, that truth 
depends upon knowledge, itself true or false ? If false, the 
position collapses. If true, how can it be itself dependent 
upon knowledge? To make it thus dependent is to incur a 
vicious circle; to make it not dependent, is again to abandon 
the position. A third difficulty is, that knowledge is not a 
simple idea, and the propositions defining it must be prior to 
the proposition that knowledge exists. 

The position rests on the same basis as the cosmological 
argument. This depends upon the existential theory of judg- 
ment, the theory, namely, that all truth consists in describing 
what exists. The dependence of truth upon knowledge is really 
a particular case of the existential theory of propositions, and 
like that theory, involves the gross assumption that what does 
not exist is nothing, or even meaningless. For truth is evi- 
dently something, and must, on this theory, be connected with 
existence. Now knowledge (perhaps) exists, and therefore it is 
convenient to make truth a property of knowledge. Thus the 
proposition, that a given proposition is true, is reduced to the 
proposition that it is known, and thus becomes existential. 
Hence Leibniz is right in connecting very closely the cosmo- 
logical argument and the argument from the eternal truths 
[e.g. G. VII. 302—5 (D. 100—103 ; L. 337—343)]. But he is 
mistaken, at least so it seems to me, in holding that truth de- 
pends upon existence. And for one who held the possible to be 
wider than the actual, this theory is quite peculiarly untenable. 

The inconsistencies, in which Leibniz is involved by the 
belief in God, are so many and various that it would take long 
to develop them all. The one which I have just mentioned is. 



PROOFS OF THE EXISTENCE OF GOD. 183 

however, among the most important. The view that the actual 
is not coextensive with the possible is, as we have seen, quite 
essential to Leibniz's doctrine of contingency and freedom, as 
well as to his solution of the problem of evil. This view is 
denied by the existential theory of judgments, upon which two 
of Leibniz's proofs of God depend. If every proposition ascribes 
a predicate to some existent, then we cannot maintain, as an 
ultimate truth, that the non-existent is possible. We can only 
mean by this that God, or some one else, believes it to be 
possible, and we must hold, if we are logical, that this belief is 
erroneous. Thus Leibniz falls, by his introduction of God, into 
a Spinozistic necessity: only the actual is possible, the non- 
existent is impossible, and the ground for contingency has 
disappeared. 

Another aspect of Spinozism is also inevitable, if God be 
conceived as having any influence on the monads. This is the 
belief in only one substance. Before developing this inconsist- 
ency, however, it will be well to examine the proof which was 
Leibniz's favourite, the proof which he himself invented, that, 
namely, from, the pre-established harmony. 

114. The proof from the pre-established harmony is a 
particular form of the so-called physico-theological proof, other- 
wise known as the argument from design. This is the argument 
of the Bridgewater Treatises, and of popular theology generally. 
Being more palpably inadequate than any of the others, it has 
acquired a popularity which they have never enjoyed. The 
world is so well constructed, we are told, that it must have had 
a highly skilful Architect. In Leibniz's form, the argument 
states that the harmony of all the monads can only have arisen 
from a common cause [e.g. G. iv. 486 (D. 79 ; L. 316)]. That 
they should all exactly synchronize, can only be explained by a 
Creator who pre-determined their synchronism. Let us see 
what this theory involves. 

There are, roughly speaking, two functions which a Chris- 
tian God has to fulfil. He has to be a Providence and a 
Creator. Leibniz merged the first of these functions in the 
second^, though he often denied that he had done so. God, he 

^ See Arnauld's objections, O, n. 15. 



184 PROOFS OP THE EXISTENCE OF GOD. 

says, is the soul's immediate external object, and is able to act 
directly on the soul, though apparently he very seldom does so 
[G. V. 99 (N. E. 109)]. This is a sense in which Leibniz agrees 
to Malebranche's doctrine, that we see all things in God [G. VI. 
578 (D. 189)]. But it is better to do away entirely with the 
immediate operation of God on the world, which is plainly 
inconsistent with Leibniz's logic. All the grounds against the 
interaction of substances are, as we saw, grounds giving meta- 
physical necessity, and therefore applying equally against God's 
action on the world. We will therefore suppose that God is 
the Creator, and that his Providence is shown only in creating 
the best possible world. 

Whenever Leibniz is not thinking of theological objections, 
he regards God's action on the world as entirely limited to 
creation. God's goodness, he says, led him to desire to create 
the good, his wisdom showed him the best possible, and his 
power enabled him to create it (G. VI. 167). God's wisdom and 
goodness correspond, roughly speaking, to knowledge and voli- 
tion in us, but his power is a peculiar attribute, to which crea- 
tures have nothing parallels God's wisdom consists of his 
knowledge of all truths, necessary and contingent alike. In so 
far as truths are necessary, his knowledge of them, which consti- 
tutes his understanding, is prior to his volitions; for his 
volitions are determined by his knowledge of the good, and all 
true propositions about the good are necessary truths. Leibniz 
perceived {e.g. G. iv. 344) that God's volitions could not signifi- 
cantly be called good, unless the good was independent of them, 
though he did not see that God's thoughts could not be signifi- 
cantly called wise, unless the truth was independent of them. 
Thus wisdom and goodness concur in creating a good world, 
since wisdom is required to know that it is good. But power 
is required for the creation of it, not for determining its nature. 
And here Leibniz seems to be guarded against inconsistency by 
the theory of contingent judgments. Every existential propo- 
sition not concerned with God is contingent, and thus, though 
God cannot, without positive contradiction, be supposed to 
affect the nature of any one substance, yet he may, without 

1 E.g. G. VI. 615 (D. 225 ; L. 244—5). But contrast G. iv. 515 (D. 125). 



PROOFS OF THE EXISTENCE OF GOD. 185 

contradiction, be supposed to cause the existence of that sub- 
stance. This is the sense in which the pre-established harmony 
is due to God. God chose to create monads which harmonized, 
and though the harmony arises from their natures, the existetice 
of monads having such natures is due to God's power. 

115. Concerning this argument, we may observe that, if 
the cosmological proof be sound, the present proof is super- 
fluous. If God's existence can be inferred from any finite 
existence, the particular nature of what exists is irrelevant, or 
is useful at most, for a subsequent empirical proof that God is 
good. Moreover, with Leibniz's conception of substance, there 
is much difficulty in the idea of creating a substance. Here he 
falls into inconsistency with the ontological argument, to which 
I must now return. 

If existence can be of God's essence — and it is necessary to 
the ontological proof that it should be so — then existence is a 
predicate of God. But if existence is a predicate of God, then 
it is a predicate. Hence, when we say anything exists, exist- 
ence is a predicate of this existent. So far, Leibniz would 
admit the argument [G. V. 339 (N. E. p. 401)]. But if existence 
be a predicate, then it is part of the nature of a substance, and 
a substance, by being created, acquires a new predicate. Hence 
the special position of existence, as a contingent and synthetic 
predicate, falls to the ground. If all substances always contain 
all their predicates, then all substances always contain or do 
not contain the predicate existence, and God must be as power- 
less over this predicate as over any other. To add the predi- 
cate existence must be metaphysically impossible. Thus either 
creation is self-contradictory, or, if existence is not a predicate, 
the ontological argument is unsound. But the other argu- 
ments, as Kant pointed out, all depend upon this argument". 
Hence if we accept it, we must regard God as the only 
substance, as an immanent pantheistic God incapable of crea- 
tion ; or, if we reject it, we must admit that all monads exist 
necessarily, and are not dependent upon any outside cause. 
This is why I said (§ 106) that monism must be pantheistic, and 
monadism must be atheistic. And so it happens that Leibniz, 

' Reine Vemunft, ed. Hartensteiri, 1867, pp. 414, 427. 



186 PROOFS OF THE EXISTENCE OF GOD. 

whenever he treats God at all seriously, falls involuntarily into a 
Spinozistic pantheism. 

116. Some of these pantheistic consequences are worth 
noting. " Everything is in God," Leibniz says, " as place is in 
that which is placed" (D. 178; F. de C. 38). Now place, in 
his system, is a mere attribute of what is placed; therefore 
things should be mere attributes of God. "God alone," we 
are told in the Monadology, "is the original simple sub- 
stance, of which all created or derivative monads are products, 
born, so to speak, from moment to moment by continual ful- 
gurations of the Deity " [G. vi. 614 (D. 225 ; L. 243)]. The 
following passage of the Discours de Mdtaphysique might almost 
have been written by Spinoza. " Created substances depend on 
God, who conserves them, and even produces them continually 
by a kind of emanation, as we produce our thoughts. For 

God views all aspects of the world in all possible ways; 

the result of each view of the universe, as if seen from a certain 
place, is a substance expressing the universe conformably to 
this point of view, if God sees fit to make his thought effective 
and produce this substance. And since God's view is always 
veritable, our perceptions are so too ; it is our judgments, 
which are from us, that deceive us " (G. IV. 439). One wonders 
what change is made when God " makes his thought effectived" 
It would seem that the sum of all substances must be indis- 
cernible from God, and therefore identical with him — the very 
creed of pantheism I Leibniz once approaches very near to 
the doctrine that all determination is negation, though he 
seems unaware that this ought to lead him to Spinozism. The 

1 Contrast the following passage in the same work (G. iv. 453): "I am not, 
however, of the opinion of some able philosophers, who seem to maintain that 
our ideas themselves are in God, and not at all in us. This comes, in my 
opinion, from their not yet having sufficiently considered what we have just 
explained here concerning substances, nor all the extent and independence of 
our soul, which causes it to contain all that happens to it, and to express God 
and with him all possible and actual beings, as an effect expresses its cause. 
Also it is an inconceivable thing that I should think by the ideas of another." 

2 It is true Leibniz assures us on the next page that God sees the universe 
not only as created substances see it, but also quite differently. But this still 
leaves all created substances indiscernible from a part of God — a view no less 
pantheistic than the other. 



PROOFS OF THE EXISTENCE OF GOD. 187 

argument is as to the necessity of a primitive force in each 
monad, of which the derivative force is a modification. Without 
primitive entelechies, he says, " there would be modifications 
without anything substantial to be modified; for what is merely 
passive could not have active modifications ; since modification, 
far from adding any perfection, can only be a variable restric- 
tion or limitation, and consequently cannot exceed the per- 
fection of the subject " (G. iii. 67). (My italics). Leibniz even 
confesses (G. II. 232) that his assertion of many substances is 
rather arbitrary. " If the notion of substance in its generic 
definition," he says, " is only applicable to the simplest or 
primitive substance, this alone will be substance. And it is 
in your power," he continues, " so to take the word substance, 
that God alone shall be substance, and other substances shall 
be called otherwise. But I prefer to seek a notion which fits 
other things, and agrees with common usage, according to 
which you, he, and I are deemed substances. You will not 
deny that this is legitimate, and, if it succeeds, useful." 

It is thus evident how wide a gulf, when God is being 
considered, there is between God, the primitive substance, and 
the monads or created substances. But when Leibniz is occu- 
pied with the monads, God has to be debased from the high 
position which pantheism gives him, and twice, at least, he is 
spoken of as one among monads (G. III. 636 ; Vil. 502). These 
two passages should, I think, be regarded as slips. The usual 
expressions for God are simple primitive substance, or primi- 
tive unity. In the two passages where God is called a monad, 
this does not occur very directly. In one, we are told that 
" monads, except the primitive one, are subject to passions " 
(G. III. 636). The other is more direct. "The monad or 
simple substance contains in its generic definition perception 
and appetition, and is either the primitive one or God, in which 
is the ultimate reason of things, or is derivative, i.e. a created 
monad" (G. vii. 502). That these two passages are to be 
regarded as slips seems likely if only because (so far as I know) 
there are no others. This is rendered still more probable by 
the fact that the traditional expression monas monadum, so far 
as I can discover, occurs nowhere. It was used by Bruno, from 
whom it used to be thought that Leibniz got the word monad. 



188 PROOFS OF THE EXISTENCE OF GOD. 

This fact seems to have led Hegel' to suppose that Leibniz also 
used the phrase, and subsequent writers, with the exception of 
Erdmann (v. Geschichte, Vol. ii. 2, p. 62), seem to have rashly 
assumed that Hegel had some authority for the supposition. 
Thus it is better not to regard Leibniz's God as one among 
monads, especially as the monads form a continuous series, and 
evidently there cannot be one differing infinitely little from 
God. 

We may now sum up the inconsistencies into which Leibniz 
is led by his theology. The ontological argument, which is alone 
capable of proving that God's existence is a necessary truth, is 
incompatible with the unique position which, where finite 
things are concerned, is assigned to existence. Leibniz's phi- 
losophy of the finite and the contingent, if it be valid, involves 
Kant's position, that existence adds nothing to the nature of 
what exists, i.e. that existence is not merely one among predi- 
cates. If this be so, existence cannot form part of any essence, 
and the ontological argument falls. The cosmological argument 
depends upon the existential theory of judgment, which is 
inconsistent with Leibniz's separation of the possible and the 
actual. For his theory of contingency, it is essential that 
something non-existent should be possible ; and this is not an 
existential judgment. The proof by means of the eternal 
truths supposes that the truth of propositions results from their 
being believed — a view which is in itself wholly false, and 
which, further, renders it quite arbitrary what propositions 
God is to believe. It also depends upon the existential theory 
of judgment, since its basis is, that truth, being as such non- 
existent, is nothing per se, but must be a mere property of 
true beliefs — a view whose circularity is self-evident. The 
argument from the pre-established harmony, again, involves 
a Creator, and the creation of substances is only possible if 
existence be not a predicate. But in that case, God's existence 
cannot be an analytic proposition, and must, on Leibniz's logic, 
be contingent. The ontological argument will be unsound, and 

1 E.g. in his history of philosophy, Werke, Vol. xvi. pp. 418, 422. Also in 
the smaller Logic, Werke, Vol. v. p. 365; Wallace's Translation, p. 334. 
Leibniz in all probability derived the word monad from his friend van Helmont. 
See Stein, Leibniz und Spinoza. 



PROOFS OF THE EXISTENCE OF GOD. 189 

God's existence itself, being contingent, must have a suflScient 
reason which inclines without necessitating. But if this be 
required, we might just as well admit the preestablished 
harmony as an ultimate fact, since the assumption of God's 
existence is insufficient for its explanation. 

117. A few words seem needed as to God's goodness. 
Most philosophers seem to suppose that, if they can establish 
God's existence, his goodness necessarily follows. Accordingly, 
though Leibniz does, in certain passages, give some argument 
for what, in a metaphysical sense, may be called God's perfec- 
tion, he nowhere takes the trouble to prove his goodness. In 
the argument submitted to Spinoza, we saw that a perfection is 
defined as any quality which is simple aud absolute, positive and 
indefinable, and expresses its object without limits (G. Vll. 261). 
Leibniz seems to have adhered to this definition of a perfection. 
Thus he says in the Monadology [§§ 40, 41 ; G. VI. 613 (D. 223 ; 
L. 239)]: "We may judge also that this supreme substance, 
which is unique, universal and necessary, having nothing out- 
side of itself which is independent of it, and being a simple 
consequence of possible being, must be incapable of limits, and 
must contain just as much reality as possible. Whence it 
follows, that God is absolutely perfect, perfection being nothing 
but the magnitude of positive reality strictly understood, setting 
aside the limits or boundaries in things which have them. 
And where there are no boundaries, that is to say, in God, 
perfection is absolutely infinite'." But perfection understood 
in this sense, though it does appear to involve God's infinite 
goodness, involves equally, except on a purely privative view of 
evil, his infinite badness. To escape this, Leibniz, like most 
optimists, asserts that evil is a limitation. God, he says, is 
infinite, the Devil is limited ; good advances ad infinitum, evil 
has bounds [G. VI. 378 (D. 196)]. Thus God's perfection in- 
volves infinite goodness, but not infinite badness. If Leibniz 



1 This seems also Leibniz's ethical sense of perfection. Cf. G. vn. 303 
(D. 101; L. 840): "Among the infinite combinations of possibles and possible 
series, that one exists by which the most of essence or of possibility is brought 
into existence."^ Also G. vii. 305 (D. 103; L. 842). But the two are distinguished 
on the next page, where moral perfection appears as a species of metaphysical 
perfection. 



190 PROOFS OF THE EXISTENCE OF GOD. 

had admitted badness to be a positive predicate, he could not 
have retained his definition of God, or his doctrine of analytic 
judgments. For good and bad would then have been not 
mutually contradictory, but yet obviously incompatible as pre- 
dicates of God. Accordingly he asserted — though without 
arguments of any kind — that badness is essentially finite. But 
this brings me to his Ethics, with the discussion of which this 
work will come to an end. 



191 



CHAPTER XVI. 



LEIBNIZ S ETHICS. 



118. In the last chapter we saw that God's goodness is 
the metaphysically necessary sufficient reason of God's good 
acts, which are contingent, and indeed the ultimate contingents 
from which all others flow. This brought us to the threshold 
of Leibniz's Ethics, in which, more even than in his doctrine of 
God, all the difficulties and inconsistencies of his system cul- 
minate. By the emphasis which he laid on final causes, he 
gave Ethics very great importance in his philosophy. And 
yet he appears to have bestowed but the smallest part of 
his thought on the meaning and nature of the good. His 
Ethics is a mass of inconsistencies, due partly to indifference, 
partly to deference for Christian moralists. Though I shall 
treat the subject briefly, I shall give it quite as large a space, 
proportionally, as it seems to have occupied in Leibniz's 
meditations. 

There are three separate questions, which I shall have to 
treat of The first two are psychological, and the last only 
is properly ethical. These are rT ^ the doctrinp, of freedom^ and 
determination, (2) the psychology of volition, (3) the nature 
of the good. 

(1) The doctrine, by which Leibniz sought to reconcile 
free will with his thorough-going determinism, depends wholly 
upon c ontingencY and the activity of substances . Freedom, 
as Leibniz points out, is a very ambiguous term. 

"Freedom of will," he says, "is... understood in two different 
senses. The first is when it is opposed to the imperfection 
or slavery of the spirit, which is a coercion or constraint, but 



192 LElBNIz's ETHICS. 

internal like that arising from the passions. The other sense 
is used when freedom is opposed to necessity." In the first 
sense, " God alone is perfectly free, and created spirits are so, 
only in proportion as they are superior to their passions. 
And this freedom properly concerns our understanding. But 
the freedom of spirit, opposed to necessity, concerns the ba re 
will, and in so far a s it is distinguish ed from ,the_urLder- 
standingi This is what is called free-will, and it consists in 
this, that we hold that the strongest reasons or impressions, 
which the understanding presents to the will, do not prevent 
the act of the will from being contingent, and do not give it 
a necessity which is absolute, and so to speak, metaphysical^" 

Of these two senses, the first corresponds to the distinction 
of activity and passivity. The will is free in so far as we are 
active, i.e. determined by distinct ideas; God alone, who has 
only distinct ideas, is perfectly free. And thus this sense is 
connected with the understanding''. The other is the sense 
which is relevant in the free-will controversy, and the one 
which must be examined now. 

Leibniz recognized — as every careful philosopher should — 
that all p sychical events haY fi— tlieir causes, just as physical 
events have, and that prediction is as possible, theoretically, 
in the one case as in the other. To this he was committed 
by his whole philosophy, and especially by the pre-established 
harmony. He points out that the future must be determined, 
since any proposition ab out _it must be already true o r^jaJse 
(G. VI. 123)! And with this, if he had not been resolved to 
rescue free will, he might have been content. The whole 
doctrine of contingency might have been dropped with ad- 
vantage. But that would have led to a Spinozistic necessity, 
and have contradicted Christian dogma. Accordingly he held 
— as the connection of the analytic and the necessary also led 
him to hold — that all existential propositions and all causal 
connections are contingent, and that consequently, though 
volitions have invariable causes, they do not follow neces- 
sarily from those causes'. He rejected entirely the liberty of 

1 N. E. pp. 179—180; G. v. 160—1, Bk. ii. Chap. xxi. 

' Cf. G. VII. 109 — 110, for further developments as to freedom in this sense. 

8 Cf. G. V. 163—4 (N. E. 183). 



Leibniz's ethics. 193 

indifference — the doctrine that the will may be uncaused — and 
even held this to be self-contradictory'. For it is necessary 
that every event should have a cause, though it is contingent 
thairthe cause-shouid'^rodu'ce its "effect: Hie~iield also that 
the indifference of equilibrium would destroy moral good and 
evil. For it would imply a choice without reason, and there- 
fore without a good or a bad reason. But it is in the goodness 
or badness of the reason that moral good and evil consist 
(G. VI. 411). He rejected also the pretended introspective 
proof of freedom, by our supposed sense of it; for, as he 
rightly says, we may be determined by insensible perceptions 
(G. Yi. 130). Fr eedom in the present sense is equally att ributed 
to God ; his volitions, though always determined by t.hp mntivB 
of th e bestTlTre none the less contingenl _Ulj^-yii. 408 — 9 ; 
Hms — 4). It may be asked why beasts and even bare monads 
are not free. For this there is, I think, no adequate ground. 
Beasts, Leibniz confesses, have spontaneity (G. vii. 109), but 
not liberty ,(G. TI. 421). Spontaneity, he says, is contingency 
without constraint, and a thing is constrained when its prin- 
ciple comes from without (G. Vll. 110). By the principle of 
a thing, I imagine Leibniz must mean the suflScient reason 
of its changes. This, then, in an animal, should be internal. 
The only sense, accordingly, in which an animal is not free, 
would seem to be that its volitions are not determined by 
knowledge of the good''. 

1 Cf. G. n. 420; iii. 401 (D. 171) ; v. 164 (N. E. 183); vii. 379. 

" Leibniz's views on this point are collected in a short paper, given by 
Gerhardt both in French and Latin (G. vii. 108 — 111). I translate from the 
French. 

"Liberty is spontaneity joined to intelligence. 

' ' Thus what is called spontaneity in beasts and in other substances destitute 
of intelligence, is raised in man to a higher degree of perfection, and is called 
liberty. 

"Spontaneity is contingency without compulsion; in other words, we call 
spontaneous what is neither necessary nor constrained. 

"We call contingent what is not necessary, or (what is the same thing) that 
whose opposite is possible, implying no contradiction. 

"Constrained is that whose principle comes from without. (Cf. Pollock's 
Spinoza, 2nd ed. p. 193. Spinoza has only the opposition free or constrained, 
not Leibniz's further distinctions.) 

"There is indifference, when there is no more reason for one than for the 

E. L. 13 



194 LEIBNIZ'S ETHICS. 

119. (2) This brings me to the psychology of volition 
and pleasure. Leibniz holds that pleasure is a sense of per- 
fection, and that what Locke calls uneasiness is essential to 
the happiness of created beings, which never consists in com- 

other. Otherwise, there would be determination. (The Latin has: And the 
determined ia opposed to it.) 

"All the actions of single substances are contingent. For it can be shown 
that, if things happened otherwise, there would be no contradiction on that 
account. 

"All actions are determined, and never indifferent. For there is always a 
reason inclining us to one rather than the other, since nothing happens without 
a reason. It is true that these inclining reasons are not necessitating, and 
destroy neither contingency nor liberty. 

" A liberty of indifference is impossible. So that it cannot be found any- 
where, not even in God. For God is determined by himself to do always the 
best. And creatures are always determined by internal or external reasons. 

"The more substances are determined by themselves, and removed from 
indifference, the more perfect they are. For, being always determined, they will 
have the determination either from themselves, and will be by so much the 
more powerful and perfect, or they will have it from without, and then they will 
be proportionally obliged to serve external things. 

"The more we act according to reason the more we are free, and there is the 
more servitude the more we act by the passions. For the more we act according 
to reason, the more we act conformably to the perfections of our own nature, 
and in proportion as we allow ourselves to be carried away by passions, we are 
slaves of external things which make us suffer. 

"To sum up: All actions are contingent, or without necessity. But also 
everything is determined or regular, and there is no indifference. We may 
even say that substances are freer in proportion as they are further removed 
from indifference and more self-determined. And that the less they have need 
of external determination, the nearer they approach to the divine perfection. 
For God, being the freest and most perfect substance, is also the most completely 
determined by himself to do the most perfect. So that Nothing {le Rien), which 
ia the most imperfect and the furthest removed from God, is also the moat 
indifferent and the least determined. Now in so far as we have lights, and act 
according to reason, we shall be determined by the perfections of our own 
nature, and oonseq^uently we shall be freer in proportion as we are less 
embarrassed as to our choice. It is true that all our perfections, and those of 
all nature, come from God, but this, far from being contrary to liberty, is rather 
the very reason why we are free, because God has communicated to us a certain 
degree of his perfection and of his liberty. Let us, then, content ourselves with 
a liberty which is desirable, and approaches that of God, which makes us the 
most disposed to choose well and act well; and let us not pretend to that 
harmful, not to say chimerical liberty, of being in uncertainty and perpetual 
embarrassment, like that Ass of Buridan, famous in the schools, who, being 
placed at an equal distance between two sacks of wheat, and having nothing 
that determined him to go to one rather than the other, allowed bimaelf to die 
of hunger." 



Leibniz's ethics. 195 

plete possession [G. v. 175 (N. E. 194) ; vii. 73 (D. 130)]. Action, 
he says, brings joy, while passion brings pain ; and action and 
passion consist in passing to a greater or less degree of per- 
fection (G. IV. 441 )\ Thus when Leibniz agrees with Locke, 
that the good is what produces pleasure [G. v. 149 (N. E. 167)], 
he is not accepting Utilitarianism, but asserting a psycho- 
logical connection between the attainment of good and the 
feeling of pleasure. In the same way he may be freed from 
the appearance of psychological hedonism, to which he ap- 
proaches dangerously near (New Essays, Bk. i. Chap. IT.). 
There are, Leibniz thinks, innate instincts, from which innate 
truths may be derived. "Although we may say truly that 
morals have indemonstrable principles, and that one of the 
first and most practical is, that we must pursue joy and shun 
sorrow, we must add that this is not a truth which is known 
purely by reason, since it is founded on internal experience, 
or on confused knowledge, for we do not feel what joy and 
sorrow are" [G. V. 81 (N. E. 86)]. "This maxim," he con- 
tinues, "is not known by reason, but, so to speak, by an 
instinct" (i6.). But reason should lead us rather to seek 
felicity, which "is only a lasting joy. Our instinct, however, 
does not tend to felicity proper, but to joy, i.e. to the present ; 
it is reason which prompts to the future and the enduring. 
Now the inclination, expressed by the understanding, passes 
into a precept or practical truth ; and if the instinct is innate, 
the truth is innate also" [G. V. 82 (N. E. 87)]". Leibniz 
seems, in this passage, to suggest that he thinks joy good 
because it is desired, and reason only useful in showing that, 
if joy be good, more joy is better than less*. But this cannot 

' Cf. Spinoza, Ethics, Part III. Prop. XI. SohoUuin: "By pleasure I shall, 
therefore, hereafter understand an affection whereby the mind passes to a 
greater perfection ; and by yain an affection whereby it passes to a less perfec- 
tion." Cf. also ih. Prop. LIX. Sohol.: "Pleasure is the passage of a man from 
less to greater perfection. Pain is the passage of a man from greater to less 
perfection." Cf. Hobbes, Human Nature, Chap. vii. (ed. Molesworth, Vol. iv.). 

" He proceeds to explain that the instincts are not necessarily practical, but 
furnish similarly the principles of the sciences and of reasoning, which are 
employed unconsciously. 

8 Cf. Spinoza, Ethics, Part III. Prop. IX. Scholium: "We have not en- 
deavour, will, appetite or desire for anything because we deem it good, but 

13—2 



196 LEIBNIZ'S ETHICS. 

be his true meaning. For, as we saw, he holds that joy is a 
sense of perfection, and therefore perfection must be distinct 
from joy. Moreover, it is a contingent truth that volition is 
determined by the good (G. ii. 38 ; iv. 438). But if volition 
is always necessarily determined by desire, as Leibniz seems 
to hold, and if the good means what is desired, then volition 
would be necessarily determined by the good. We must 
suppose, therefore, that Leibniz considers it a synthetic and 
contingent proposition that we desire the good, and does not 
commit the fallacy of supposing that the good means the 
desired. This appears also from a passage where Leibniz 
points out that God's will could not have the good for its 
effect, unless it had it for its object, and that the good is 
therefore independent of God's will (G. iv. 344) ; or from the 
explanation that God's goodness made him desire to create 
the good, while his wisdom showed him the best possible 
(G. VI. 167). 

120. The question of sin is one which is very inconvenient 
for Leibniz's theory of volition. Virtue, he says, is an un- 
changeable disposition to do what we believe to be good. 
Since our will is not led to pursue anything, except as the 
understanding presents it as good, we shall always act rightly 
if we always judge rightly (G. vii. 92). We pursue the greatest 
good we perceive, but our thoughts are for the most part surd, 
i.e. mere empty symbols ; and such knowledge cannot move us 
[G. V. 171 (N. E. 191)]. And similarly vice is not the force of 
action, but an impediment to it, such as ignorance (G. ii. 317). 
In fact, original sin and materia prima are almost indis- 
tinguishable. From this basis he sets about manufacturing 
immorality. It is evident that, had he been consistent, he 
would have said boldly, all sin is due wholly to ignorance. 
Instead of this, what he does say is that we must make a 
rule to follow reason, though perceived only by surd thoughts 
[G. V. 173 (N. E. 193)] ; that it depends upon us to take pre- 
cautions against surprises by a firm determination to reflect, 
and only to act, in certain junctures, after having thoroughly 

contrariwise deem a thing good because we have an endeavour, will, appetite, 
or desire for it.'' Cf. also ih. Prop. XXXIX. Schol. It seems probable that 
Leibniz was confused in his own mind as regards this alternative. 



LEIBNIZ'S ETHICS. 197 

deliberated (G. iv. 454) ; that the chief rule of life is, always 
to do, not what the passions (Bewegungen), but what the 
understanding indicates as the most useful, and when we 
have done it, to account ourselves happy however it turns 
out (G. VII. 99). All these remarks are discreditable subter- 
fiiges to conceal the fact that all sin, for Leibniz, is original 
sin, the inherent finitude of any created monad, the con- 
fusedness of its perceptions of the good, whence it is led, in 
honest and unavoidable delusion, to pursue the worse in place 
of the better. We cannot make a rule to follow reason, unless 
we perceive that this rule is good ; and if we do perceive this, 
we certainly shall make the rule. His determinism has gone 
too far for morality and immorality, though it in no way 
interferes with goodness and badness. 

121. (3) This brings me to the nature and meaning of 
good and evil themselves in Leibniz. He distinguishes three 
kinds of good and evil, metaphysical, moral and physical. The 
theory of metaphysical good and evil is clear and consistent, 
and harmonizes with the rest of his system ; but there is no 
obvious ethical meaning in it. The other two seem less fun- 
damental, and are sometimes treated as mere consequences of 
metaphysical good and evil. Thus Leibniz's Ethics, like many 
other ethical systems, suffers from non-existence. Something 
other than good is taken as fundamental, and the deductions 
from this are taken as having an ethical imports 

" Evil," we are told, " may be taken metaphysically, physi- 
cally, and morally. Metaphysical evil consists in simple imper- 
fection, physical evil in suffering, and moral evil in sin. Now 
although physical and moral evil are not necessary, it is enough 
that, in virtue of the eternal truths, they are possible. And 
as this immense region of Truths contains all possibilities^, there 

1 The theory of metaphysical good and evil was derived from Spinoza, and 
was earlier than the rest of Leibniz's Ethics. It was capable of purely logical 
development, and did not involve the appeal to final causes which, after 1680, 
Leibniz perpetually supported by an allusion to Plato's Phaedo {v. Stein, op. cit. 
p, 118 ff.). The clearest statement of the principle of metaphysical perfection 
occurs in an undated paper (G. vii. 194 — 7), written probably about the year 
1677 {v. G. VII. 41 — 2), though agreeing exactly in this respect with The ultimate 
Origination of things, e.g. G. vii. 303 (L. 340; D. 101). See Appendix, § 121. 

2 This passage proves, what might otherwise be doubtful, that Leibniz realized 
that propositions about possible contingents are necessary. See p. 26 supra. 



198 Leibniz's ethics. 

must be an infiDity of possible worlds, evil must enter into 
several of them, and even the best of all must contain evil ; 
this is what has determined God to permit evil" (G. VI. 115). 
This gives Leibniz's solution of the problem of evil, and it 
is plain that metaphysical evil is the source of the whole. The 
following passage leaves this beyond doubt. " We ask first, 
whence comes evil ? If God is, whence the evil ? if he is not, 
whence the good? The ancients attributed the cause of evil 
to matter, which they believed increate and independent of 
God ; but we, who derive all things from God, where shall we 
find the source of evil ? The answer is, that it must be sought 
in the ideal nature of the creature, inasmuch as this nature 
is contained among eternal truths, which are in the under- 
standing of God, independently of His will. For we must 
consider that there is an original imperfection in the creature, 
anterior to sin, because the creature is essentially limited; 
whence it comes that the creature cannot know everything, 
and can be mistaken and commit other faults" (G. vi. 114 — 5). 
And hence Leibniz rejects Des Cartes' principle, that errors 
depend more on the will than on the intellect [G. IV. 361 
(D. 52)]. 

122. Thus metaphysical evil, or limitation — though 
Leibniz hesitates to declare this openly — is the source of sin 
and pain. And this is sufficiently evident. For if we always 
judged rightly, we should always act rightly; but our mis- 
judgment comes from confused perception, or materia prima, 
or limitation. And pain accompanies passage to a lower per- 
fection, which results from wrong action. Thus physical and 
moral evil both depend upon metaphysical evil, i.e. upon 
imperfection or limitation. Leibniz does not usually speak 
of the opposite of this as metaphysical good, but as meta- 
physical perfection. Many of his arguments, however, involve 
the assumption that metaphysical perfection is good, as when 
he argues against a vacuum \ or when he urges that " among 
the infinite combinations of possibles and possible series, that 
one exists by which most of essence or of possibility is brought 
into existence ^" The same view seems implied in a passage 

1 E.g. G. vn. 377 (D. 253) ; but contrast G. n. 475. 

'■* G. VII. 303 (D. 101 ; L. 340). See also the preceding sentence. 



LEIBNIZ'S ETHICS. 199 

which incidentally defines metaphysical perfection. " As pos- 
sibility," he says, " is the principle of essence, so perfection, 
or the degree of essence (by which as many things as possible 
are compossible), is the principle of existence." And in the 
preceding sentence he has used imperfection and moral 
absurdity as synonyms [G. Vli. 304 (D. 103; L. 342)]. And 
on the next page, where he endeavours to distinguish meta- 
physical and moral perfection, he only succeeds in making the 
latter a species of the former. "And in order," he explains, 
"that no one should think that we here confound moral per- 
fection, or goodness, with metaphysical perfection, or greatness, 
and should admit the latter while denying the former, it 
must be known that it follows from what has been said that 
the world is the most perfect, not only physically, or, if you 
prefer it, metaphysically, because that series of things has 
been produced in which the most reality is actualized, but 
also morally, because, in truth, moral perfection is physical 
perfection for minds themselves " [G. vii. 306 (D. 104 ; L. 345)]. 
That is to say, moral perfection is right action, and this 
depends upon physical perfection for minds, i.e. upon clear 
perception'. 

On the relation of metaphysical and moral perfection, 
Leibniz can with difficulty be cleared of dishonesty. He uses 
the dependance of the latter on the former to solve the 
problem of evil, and to show that evil is a mere limitation. 
This last is essential, as we saw in the preceding chapter, to 
his proof of God's goodness, and to his whole connection of evil 
with materia prima and finitude. But he endeavours to make 
moral evil independent, as soon as he thinks of sin, punish- 
ment, and responsibility, of Heaven and Hell, and the whole 
machinery of Christian moralists. If anything is to be made of 
his Ethics, we must boldly accept the supremacy of metaphysical 
perfection and imperfection, and draw the consequences. 

Metaphysical perfection is only the quantity of essence 
[G. VII. 303 (D. 101 ; L. 340)], or the magnitude of positive 

' Of. also the foUowing passage (G. iii. 32): "Metaphysical good and evil is 
perfection or imperfection in the universe, hut is specially understood of those 
good and evil things which happen to creatures that are unintelligent, or so 
to speak unintelligent." 



200 LEiBNIz's ETHICS. 

reality [G. vi. 613 (D. 224 ; L. 240)]. This means the pos- 
session of all possible simple predicates in the highest possible 
degree. Leibniz asserts, against Spinoza, that one thing may 
have more reality than another by merely having more of one 
attribute, just as well as by having more attributes. For 
instance, he says, a circle has more extension than the inscribed 
square [G. i. 144 (D. 17)]. But in another place he asserts 
that things not capable of a highest degree, such as numbers 
and figures, are not perfections (G. IV. 427). As he also asserts 
that God is infinite, while the Devil is finite, that good advances 
ad infinitum, while evil has its bounds [G. vi. 378 (D. 196)], 
numbers and figures are evidently excluded because they are 
not true predicates, and because, as we saw in discussing the 
continuum, infinite number is self-contradictory, though the 
actual infinite is permissible. Thus metaphysical perfection 
consists in having as many predicates as possible in as high 
a degree as possible, and no true predicates are excluded from 
this definition^ 

From this it follows, of course, that imperfection is some- 
thing merely negative, namely, the mere absence of perfection. 
Thus monads differ from God only as less and more; they 
have the same perfections as God has, but in a lower degree 
(G. II. 125)". The Devil, on this view, should be the lowest 
of bare monads — a view which theologians would scarcely 
accept, since they always suppose him capable of knowledge. 
There is one passage where Leibniz endeavours directly to 
connect perfection with good. "It being once posited," he 
says, "that being is better than not-being, or that there is 
a reason why something should be rather than nothing, or 
that we must pass from possibility to actuality, it follows 
that, even in the absence of every other determination, the 
quantity of existence is as great as possible" [G. Vli. 304 
(D. 102; L. 341)]. Thus he seems to admit that goodness 
means something different from quantity of existence, and to 
regard the connection of the two as significant. 

1 Of. also G. V. 15 (D. 95; N. E. 15). 

^ Of. Spinoza, Ethics, Part II. Prop. XLIX. Scholium: "We are partakers 
of the Divine Nature in proportion as our actions become more and more 
perfect, and we more and more understand God." Also Monadology, § 42. 



Leibniz's ethics. 201 

123. The Ethics to which this view leads is a common 
one. Goodness and Reality are held to go hand in hand, if 
not to be synonymous^ Hence it easily follows that Eeality 
is good ; aad this consequence is, so far as I can discover, the 
sole recommendation of such an Ethics. For Leibniz especially, 
who admits the existence of evil [G. vi. 376 (D. 194)], such a 
view is absurd. For if evil be a mere limitation, all that 
exists is good in different degrees, and never evil in any degree 
at all. If any existent, such as pain, be pronounced evil, it 
follows that evil is a positive predicate, like good^ Hence 
it will be included in metaphysical perfection. The doctrine 
of analytic judgments must have contributed to the view that 
evil is a mere negation. For it is obvious that good and 
bad are incompatible predicates, and if both are positive, this 
is a synthetic judgment. Hence evil was regarded as the mere 
negation of good, though it would have been equally logical 
to regard good as the mere negation of evil. When once it 
is recognized that evil is a positive predicate, the whole 
privative theory of evil falls, and with it the connection of 
metaphysical and ethical perfection, as also the definition of 
God as having all positive predicates. 

124. There remains one minor inconsistency which must 
be noticed. Leibniz speaks often as if final causes had ex- 
clusive reference to spirits [G. iv. 480 (D. 73; L. 304)], but 
at other times definitely denies this {e.g. G. Vi. 168). He seems 
to hold that only spirits, among monads, are ends in them- 
selves ; other ends are not individual monads, but metaphysical 
good, the order and beauty of nature. The first principle of 
the physical world, he says, is to give it as much perfection 
as possible, and of the moral world, or City of God, to give it 
the greatest possible felicity (G. IV. 462). This leads to a 
harmony between the kingdoms of Nature and of Grace, be- 
tween God as Architect and God as Monarch (G. vi. 605 (D. 215 ; 
L. 421)]. In the first, he seeks only order and metaphysical 

1 Cf. Spinoza, Ethics, Part II. Def. VI.: "By reality and perfection I under- 
stand the same thing." 

2 Even in 1677, when Leibniz was as near as at any time to Spinozism, he 
urges against a Cartesian that " both pleasure and pain are something positive" 
(G. I. 214). Cf. Stein, op. cit. pp. 90, 91. 



202 LEIBNIZ'S ETHICS. 

perfection ; in the second, he seeks the happiness of spirits. 
But so well is the world contrived, that the two ends lead 
to the same series of events, and in this again we have a 
pre-established harmony. 

In Leibniz's philosophy everything, from the Law of Suf- 
ficient Reason onwards, depends, through the introduction of 
final causes, upon Ethics. But Ethics, being a subject on 
which theology is very definite, could not be dealt with by 
Leibniz in a free spirit. The Ethics to which he was entitled 
was very similar to Spinoza's; it had the same fallacies, and 
similar consequences. But being the champion of orthodoxy 
against the decried atheist, Leibniz shrank from the conse- 
quences of his views, and took refuge in the perpetual iteration 
of edifying phrases. The whole tendency of his temperament, 
as of his philosophy, was to exalt enlightenment, education, 
and learning, at the expense of ignorant good intentions. 
This tendency might have found a logical expression in his 
Ethics. But he preferred to support Sin and Hell, and to 
remain, in what concerned the Church, the champion of igno- 
rance and obscurantism. This is the reason why the best parts 
of his philosophy are the most abstract, and the worst those 
which most nearly concern human life. 



APPENDIX. 



.-^R?: 



EXTRACTS FROM LEIBNIZ 

CLASSIFIED ACCORDING TO SUBJECTS. 



II. § 8. Outline of Leibniz's logical argument. 

G. II. 46 (1686). In consulting the notion which I have of 
every true proposition, I find that every predicate, necessary or 
contingent, past, present, or future, is comprised in the notion of 

the subject, and I ask no more The proposition in question is 

of great importance, and deserves to be well established, for it 
follows that every soul is as a world apart, independent of every- 
thing else except God ; that it is not only immortal and so to speak 
impassible, but that it keeps in its substance traces of all that 
happens to it. It follows also in what consists the intercourse of 
substances, and particularly the union of soul and body. This 
intercourse does not happen according to the ordinary hypothesis 
of the physical influence of one on the other, for each present state 
of a substance comes to it spontaneously, and is only a consequence 
of its previous state. It does not happen either according to the 

hypothesis of occasional causes, but it happens according to the 

hypothesis of concomitance, which appears to me demonstrative. 
That is to say, each substance expresses the whole sequence of the 
universe according to the view or respect which is proper to it, 
whence it happens that they perfectly agree together. 

II. § 10. Are all propositions reducible to the subject- 
predicate form ? 

G. II. 240. There is no denomination so extrinsic as not to 
have an intrinsic one for its foundation. 

G. II. 250. Things which differ in place must express their 
place, i.e. the surrounding things, and thus be distinguished not 
only by place, or by a mere extrinsic denomination, as such things 
are commonly conceived. 



206 THE LAW OF CONTRADICTION. 

G. V. 129 (N. E. 144). In my view, relation is more general 
than comparison. For relations are either of comparison or con- 
currence (concours). The former concern agreement (convena'nce) or 
disagreement (I take these terms in a less wide sense), which com- 
prehends resemblance, equality, inequality, etc. The second class 
involve some connection, as of cause and effect, whole and parts, 
situation and order, etc. 

G. V. 210 (N. E, 235). Relations and orders partake of the 
nature of rational entities (ont quelque chose de I'etre de raison), 
although they have their foundation in things ; for it may be said 
that their reality, like that of eternal truths and of possibilities, 
comes from the supreme reason. 

G. V. 377 (N. E. 451). It is better to place truths in the 
relation between the objects of ideas, which causes one to be com- 
prised or not comprised in the other. 

G. V. 378 (N. E. 452). Let us be content to seek truth in 
the correspondence of the propositions, which are in the mind, with 
the things concerned. 

G. II. 233. For my part, I do not think it possible that there 
should be an A and a B having no common predicate. It does not 
follow, however, if two predicates concurring to form the concept 
of C are separable, that there is not some one concept of 0. H.g. a 
square is an equilateral rectangle, but the rectangle can be separated 
from the equilateral..., and the equilateral from the rectangle..., 
and yet a square is one figure and has one concept. 

G. II, 486. You wUl not, I believe, admit an accident which 
is in two subjects at once. Thus I hold, as regards relations, that 
paternity in David is one thing, and filiation in Solomon is another, 
but the relation common to both is a merely mental thing, of which 
the modifications of singulars are the foundation. 

II. § 11. Analytic and synthetic propositions. 

G. V. 92 (N. E. 99). Far from approving the acceptance of 
doubtful principles, I would have people seek even the demonstra- 
tion of the axioms of Euclid And when I am asked the means of 

knowing and examining innate principles, I reply that, except 

instincts whose reason is unknown, we must try to reduce them to 
first principles, i.e. to axioms which are identical or immediate by 
means of definitions, which are nothing but a distinct exposition of 
ideas. 

G. V. 342 (N. E. 403). It is not the figures which make the 



THE LAW OF CONTBADICTION. 207 

proof with geometers... It is the universal propositions, i.e. the defi- 
nitions, the axioms, and the theorems already proved, which make 
the reasoning, and would maintain it even if there were no figure. 

6. v. 343 (N. E. 404). The primitive truths, which are 
known by intuition, are, like the derivative, of two kinds. They 
are among the truths of reason or the truths of fact. Truths of 
reason are necessary, and those of fact are contingent. The primi- 
tive truths of reason are those which I call by the general name of 
identicals, because it seems that they only repeat the same thing, 
without teaching us anything. Those which are affirmative are 
such as the following : everything is what it is, and in as many 

examples as we may desire, A is A, B is B The equilateral 

rectangle is a rectangle If the regular four-sided figure is an 

equilateral rectangle, this figure is a rectangle If A is not-B, 

it follows that A is not-B I come now to the negative identi- 
cals, which depend either upon the principle of contradiction or 
upon that of disparates. The principle of contradiction is in 
general : A proposition is either true or false. 

G. V. 347 (N. E. 410). As for the proposition that three is 

equal to two and one, ...it is only the definition of the term three 

It is true there is in this a hidden enunciation, ...namely, that these 
ideas [of numbers] are possible ; and this is here known intuitively, 
.so that we may say intuitive knowledge is contained in definitions 
when their possibility is immediately evident. 

G. VI. 323. The triple number of dimensions is determined 
[in matter], not by the reason of the best, but by a geometrical 
necessity ; it is because geometers have been able to show that there 
are only three mutually perpendicular straight lines which can 
intersect in the same point. Nothing could be chosen more appro- 
priate for showing the difierence there is between moral necessity, 
which governs the choice of the sage, and the brute necessity of 
Strato and the Spinozists, ...than to cause people to consider the 
difierence between the reason of the laws of motion, and the reason 
of the triple number of dimensions : the first consisting in the 
choice of the best, the second in a geometric and blind necessity. 

G. IV. 367 (D. 48). The first of the truths of reason is the 
principle of contradiction, or, what comes to the same thing, that of 
identity. 

G. VI, 612 (D. 223 ; L. 236). Truths of reasoning are neces- 
sary and their opposite is impossible : truths of fact are contingent 
and their opposite is possible. When a truth is necessary, its 



208 THE LAW OF SUFFICIENT REASON. 

reason can be found by analysis, resolving it into simpler ideas 

and truths, until we come to those that are primary Primary 

principles... cannot be proved, and indeed have no need of proof; 
and these are identical enunciations, whose opposite involves an 
express contradiction. 

G. VII. 355 (D. 239). The great foundation of mathematics 

is the principle of contradiction And this principle alone suffices 

for proving all Arithmetic and all Geometry, i.e. all mathematical 
principles. But in order to proceed from mathematics to natural 
philosophy another principle is requisite'. . .' : I mean the principle of 
a sufficient reason. 

G. III. 400 (D. 170). -A- truth is necessary when the opposite 
implies contradiction ; and when it is not necessary it is called 
contingent. That God exists, that all right angles are equal to 
each other, are necessary truths ; but it is a contingent truth that 
I exist, or that there are bodies which show an actual right angle. 

G. I. 384. In order to be assured that what I conclude from a 
definition is true, I must know that this notion is possible. For if 
it implies a contradiction, we may at the same time draw opposite 
conclusions from it. ...This is why our ideas involve a judgment. 

G. V. 21 (N. E. 21). Ideas and truths can be divided into 
such as are primitive and such as are derivative ; the knowledge of 
those that are primitive does not need to be formed, but only to be 
distinguished. 

G. III. 443. Definitions are not arbitrary, as Hobbes believed, 
and we cannot form ideas as we like, though it seems that the Car- 
tesians are of this opinion. For it is necessary that these ideas which 
we undertake to form should be veritable, i.e. possible, and that the 
ingredients which we put into them should be compatible inter se. 

III. § 13. The range of contingent judgments in Leihniz. 

G. V. 428 (N. E. 515). As for the eternal truths, it is to be 
observed that at bottom they are all hypothetical, and say in fact : 
Such a thing being posited, such another thing is. 

G. III. 400 (D. 171). Although all the facts of the universe 
are now certain in relation to God, or (what comes to the same 
thing) determined in themselves and even interconnected, it does 
not follow that their connection is always truly necessary, i.e. that 
the truth, which pronounces that one fact follows from another, 
is necessary. And this must be especially applied to voluntary 
actions. 



THE LAW OF SUFFICIENT REASON. 209 

G. VI, 123. Philosophers agree now-a-days that the truth of 
future contingents is determined, i.e. that future contingents are 
future, or that they will be. ...Thus the contingent, though future, is 
none the less contingent ; and determination, which would be called 
certainty if it were known, is not incompatible with contingency. 

G. II. 39 (1686). The notion of a species involves only eternal 
or necessary truths, but the notion of an individual involves, sub 
ratione possibilitatis, what is of fact, or related to the existence of 
things and to time, and consequently depends upon certain free 
decrees of God considered as possible ; for truths of fact or of exist- 
ence depend upon the decrees of God. 

G. II. 40 (1686). I believe there are only a few free primitive 
decrees, which regulate the consequences of things, which, joined to 
the free decree creating Adam, decide the result. 

G. IV. 437 (1686). Connection or consecution is of two sorts : 
the one is absolutely necessary, so that its contrary implies contra- 
diction, and this deduction occurs in eternal truths, such as are 
those of geometry ; the other is only necessary ex hypothesi, and 
so to speak by accident, and it is contingent in itself, when the 
contrary does not imply contradiction. 

G. III. 54 (D. 35). The true Physics must really be derived 
from the source of the Divine perfections. ...Far from excluding 
final causes, and the consideration of a Being acting with wisdom, 
it is hence that everything in Physics must be deduced. 

G. III. 645. [Dynamics] is to a great extent the foundation 
of my system ; for we there learn the difference between truths 
whose necessity is brute and geometric, and truths which have their 
source in fitness and final causes. 

G. VI. 319. The laws of motion which actually occur in 
nature, and are verified by experiments, are not in truth absolutely 
demonstrable, as a geometrical proposition would be : but also it is 
not necessary that they should be so. They do not spring entirely 
from the principle of necessity, but they spring from the principle 
of perfection and order ; they are an effect of the choice and wisdom 
of God. 



III. § 14. Meaning of the principle of sufficient reason. 

G. VII. 309. There are two first principles of all reasonings, 
the principle of contradiction... and the principle that a reason must 
be given, i.e. that every true proposition, which is not known per se, 

E. L. U 



210 THE LAW OF SUFFICIENT REASON. 

has an & priori proof, or that a reason can be given for every truth, 
or, as is commonly said, that nothing happens without a cause. 
Arithmetic and Geometry do not need this principle, but Physics 
and Mechanics do, and Archimedes employed it. [In a marginal 
note Leibniz remarks :] The true cause, why certain things exist 
rather than others, is to be derived from the free decrees of the 
divine will, the first of which is, to will to do all things in the best 
possible way. 

Gr. VII. 374 (D. 250). When two things which cannot both 
be together, are equally good ; and neither in themselves, nor by 
their combination with other things, has the one any advantage 
over the other ; God will produce neither of them. 

Gr. IV. 438 (1686). This demonstration of this predicate of 
Caesar [that he resolved to cross the Rubicon] is not as absolute as 
those of numbers or of Geometry, but presupposes the series of 
things which God has chosen freely, and which is founded on the 
first free decree of God, namely, to do always what is most perfect, 
and on the decree which God has made (in consequence of the first), 
in regard to human nature, which is that man will always do 
(though freely) what appears best. Now every truth which is 
founded on decrees of this kind is contingent, although it is certain. 
...All contingent propositions have reasons for being as they are 
rather than otherwise, or (what is the same thing) they have d, priori 
proofs of their truth, which render them certain, and show that the 
connection of subject and predicate in these propositions has its 
foundation in the nature of the one and the other ; but they do not 
have demonstrations of necessity, since these reasons are only 
founded on the principle of contingency, or of the existence of 
things, i.e. on what is or appears the best among several equally 
possible things. 

G. II. 40 (1686). As there are an infinity of possible worlds, 
there are also an infinity of laws, some proper to one, others to 
another, and each possible individual of any world contains in its 
notion the laws of its world. 

G. VII. 199. In demonstration I use two principles, of which 
one is that what implies contradiction is false, the other is that a 
reason can be given for every truth (which is not identical or imme- 
diate), i.e. that the notion of the predicate is always expressly or 
implicitly contained in the notion of its subject, and that this holds 
good no less in extrinsic than in intrinsic denominations, no less in 
contingent than in necessary truths. 



THE LAW OF SUFFICIENT REASON. 211 

III. § 15. Its relation to the law of contradiction. 

G. Vli. 419 (D. 285). Is this [the principle of sufficient 
reason] a principle that wants to be proved 1 

G, VII. 364 (D. 244). It appears from what I have said, that 
my axiom has not been well understood ; and that the author 
[Clarke] denies it, though he seems to grant it. 'Tis true, says he, 
that there is nothing without a sufficient reason... but he adds, that 
this sufficient reason is often the simple or mere will of G^orf. ...But 
this is plainly maintaining that God wills something, without any 
sufficient reason for his will : against the axiom, or general rule of 
whatever happens. This is falling back into the loose indifference, 
which I have confuted at large, and showed to be absolutely 
chimerical, even in creatures, and contrary to the wisdom of God, 
as if he could operate without acting by reason. 

G. II. 56 (1686). If we were absolutely to reject pure pos- 
sibles, we should destroy contingency and liberty ; for if there were 
nothing possible but what God actually creates, what God creates 
would be necessary, and if God wished to create something, he 
"could only create that7 without liberty of choice. 

G. II. 423. When any one has chosen in one way, it would 
not imply^a contradiction if he had chosen otherwise, because the 
determining reasons do not necessitate (the action). 

G. II. 181. I think you will concede that not everything 
possible exists — But when this is admitted, it follows that it is not 
from absolute necessity, but from some other reason (as good, order, 
perfection) that some j)ossibles obtain existence rather than others. 

G. II. 49 (1686). Notions of mdmduar'snbstaQeevwhieh-are 
compl ete and capable of wholly distinguishing thei r subject, and 
involve consequently contingent truths or truths of fact, and in- 
dividual cir cumstances of time, place, etc. . must also involve in 
tHar notion, taken as possible, the free decrees of God, also taken 
as possible, bec ause these free decrees are th e principal sources of 
existents or facts ; whereas essences are in the Divine understand- 
ing before the consideration of the will. 

G. IV. 344. In maintaining that the eternal truths of geome- 
try and morals, and consequently also the rules of justice, goodness, 
and beauty, are the effect of a free or arbitrary choice of the will of 
God, it seems that he is deprived of his wisdom and justice, or 
rather of his understanding and will, having left only a certain 
unmeasured power from which all emanates, which deserves rather 

14—2 



212 THE CONCEPTION OF SUBSTANCE. 

the name of nature than that of God ; for how is it possible that 
his understanding (whose object is the truths of the ideas contained 
in his essence) can depend upon his will 1 And how can he have a 
will which has the idea of the good, not for its object, but for its 
effect? 

G. II. 424. In my opinion, if there were no best possible 
series, God would have certainly created nothing, since he cannot 
act without a reason, or prefer the less perfect to the more perfect. 

IV. § 16. Cartesian and Spinozistic views on substance. 

G. VI. 581. [Dialogue between Philarfete (Leibniz) and Ariste 
(Malebranche).] Ariste. All that can be conceived alone, and 
without thinking of anything else, or without our idea of it repre- 
senting something else, or what can be conceived alone as existing 
independently of anything else, is a substance. . . . 

G. VI. 582. Philarete. This definition of substance is not 
free from difficulties. At bottom there is nothing but God that 
can be conceived as independent of other things. Shall we say 
then, with a certain innovator who is but too well known, that God 
is the only substance, of whom creatures are mere modifications! 
If you restrict your definition, by adding that substance is what can 
be conceived independently of every other creature, we shall 
perhaps find things which, without being substances, have as much 
independence as extension. For example, the force of action, life, 
antitypia, are something at once essential and primitive, and we can 
conceive them independently of other notions, and even of their 
subjects, by means of abstractions. On the contrary, subjects are 
conceived by means of such attributes 

Ariste Let us say that the definition must be only understood 

of concretes ; thus substance will be a concrete independent of every 
other created concrete. 

G. VI. 585. PhilarHe There is nothing but monads, i.e. 

simple or indivisible substances, which are truly independent of 
every other created concrete thing. [Contrast G. iv. 364, quoted in 
Appendix, iv. § 17.] 

G. II. 249. I do not at all approve the doctrine of attributes 
which people form now-a-days, according to which some one simple 
absolute predicate, which they call an attribute, constitutes a sub- 
stance ; for I find among notions no predicates wholly absolute, or 
not involving connection with others. Certainly thought and exten- 



THE CONCEPTION OF SUBSTANCE. 213 

sion, which are commonly alleged as examples, are nothing less than 
such attributes, as I have often shown. Nor is the predicate, unless 
taken in the concrete, identical with the subject ; and thus a mind 
coincides (though not formally) with the thinker, but not with 
thought. For it belongs to the subject to involve, besides the 
present, future and past thoughts also. 



IV. § 17. The meaning of substance in Leibniz. 

G. II. 12 (1686). Since the individual notion of each person 
involves, once for all, what will happen to him for ever, we see here 
the d, priori proofs or reasons of the truth of each event, or why one 
has happened rather than the other. But these truths, though 
certain, are none the less contingent, being founded on the free will 
of God and of creatures. It is true that their choice always has 
reasons, but they incline without necessitating. 

G. II. 37 (1686). Mons. Arnaud finds strange what it seems 
that I maintain, namely, that all human events follow with hypo- 
thetical necessity from the sole supposition that God chose to create 
Adam ; to which I have two answers to give, the one, that my 
supposition is not merely that God chose to create an Adam, whose 
notion was vague and incomplete, but that God chose to create such 
and such an Adam, sufficiently determined for an individual. And 
this individual complete notion, according to me, involves relations 
to the whole series of things The other reply is, that the conse- 
quence, in virtue of which the events follow from the hypothesis, is 
indeed always certain, but is not always necessary with a meta- 
physical necessity, as is that which is found in M. Arnaud's example 
(that God, in resolving to create me, could not fail to create a 
nature capable of thought), but that often the consequence is only 
physical, and presupposes certain free decrees of God, as do conse- 
quences depending on the laws of motion, or on this principle of 
morals, that every spirit will pursue what seems to it the best. 

G. IV. 432 (1686). It is rather difficult to distinguish the 
actions of God from those of creatures ; for there are some who 
believe that God does everything, while others imagine that he only 
preserves the force which he has given to creatures : the sequel will 
show how both may be said. Now since actions and passions 
belong properly to individual substances (actiones sunt supposito- 
rum), it would be necessary to explain what such a substance is. 
It is true, indeed, that when several predicates can be attributed to 



214 THE CONCEPTION OF SUBSTANCE. 

the same subject, and this subject can no longer be attributed to any- 
other, -we call it an individual substance ; but that is not enough, 
and such an explanation is only nominal. We must therefore con- 
sider what it is to be truly attributed to a certain subject. Now it 
is certain that every true predication has some foundation in the 
nature of things, and when a proposition is not identical, i.e. when 
the predicate is not expressly contained in the subject, it must be 
contained in it virtually, and this is what philosophers call irt-esse, 
by saying that the predicate is in the subject. Thus the subject- 
term must always contain the predicate-term, so that one who 
perfectly understood the notion of the subject would judge also that 
the predicate belongs to it. This being so, we may say that the 
nature of an individual substance, or complete being, is to have a 
notion so completed that it suffices to comprehend, and to render 
deducible from it, all the predicates of the subject to which this 
notion is attributed. Thus the quality of king, which belongs to 
Alexander the Great, abstracting from the subject, is not sufficiently 
determined for an individual, and does not involve the other quali- 
ties of the same subject, nor all that the notion of this Prince 
contains, whereas God,' seeing the individual notion or hecceity of 
Alexander, sees in it at the same time the foundation and the reason 
of all the predicates which can truly be attributed to him, as e.g. 
whether he would conquer Darius and Porus, even to knowing 
d. priori (and not by experience) whether he died a natural death or 
by poison, which we can only know by history. 

G. II. 54 (1686). There would be several Adams disjunctively 
possible... whatever finite number of predicates incapable of deter- 
mining all the rest we may take, but what determines a certain 
Adam must involve absolutely all his predicates, and it is this 
complete notion which determines the general into the individual 
(rationeni generalitatis ad individuum). 

G. V. 96 (N. E. 105). I am of opinion that reflection suffices 
for finding the idea of substance in ourselves, who are substances. 

G. V. 137 (N. E. 154). I believe that the consideration of 
substance is one of the most important and fruitful points in 
philosophy. 

G. V. 274 (N. E. 316). I am not of your opinion that in this 
[as regards real and nominal definitions] there is a diflerence 
between the ideas of substances and the ideas of predicates, as if 
the definitions of predicates... were always real and nominal at the 
same time, while those of substances were nominal only We 



THE CONCEFnON OF SUBSTANCE. 215 

have a knowledge of true substances or unities (as God and the 
soul) as intimate as we have of most of the modes. Moreover there 
are predicates as little known as the contexture of bodies. 

6. IV. 364 (D. 55). I know not whether the definition of 
substance as that which needs the concurrence of God only for its 
existence, is appropriate to any created substance known to us, 
unless interpreted in a somewhat unusual sense. For we need not 
only other substances, but also, much more, our accidents. Since, 
therefore, substance and accident mutually require each other, 
there will be need of other criteria for distinguishing substance 
from accident, among which this may be one, that a substance, 
though it does need some accident, yet often has no need of one 
determinate accident, but when this is taken away, is content with 
the substitution of another ; whereas an accident does not need 
merely some substance in general, but also that one of its own in 
which it once inheres, so as not to change it. There remain, however, 
other things to be said elsewhere of the nature of substance, which 
are of greater moment and require a more profound discussion. 

G. IV. 469 (D. 69). The notion of substance, which I assign, 
is so fruitful that from it follow primary truths, even those concern- 
ing God and minds and the nature of bodies. 

G. VI. 493 (D. 151). Since I conceive that other beings have 
also the right to say /, or that it may be said for them, it is by this 
means that I conceive what is called substance in general. 

G. VI. 350. What does not act, does not deserve the name of 
substance. 

G. II. 45 (1686). In order to judge of the notion of an indi- 
vidual substance, it is well to consult that which I have of myself, 
as we must consult the specific notion of the sphere to judge of its 
properties. 

G. III. 247. I believe that we have a clear but not a distinct 
idea of substance, which comes in my opinion from the fact that we 
have the internal feeling of it in ourselves, who are substances. 

G. II. 43 (1686). Let ABC be a line representing a certain 
time. And let there be a certain individual substance, for example 
myself, which la,sts or subsists during this time. Let us then take 
first me who subsist during the time AB, and also me who subsist 
during the time BC. Since then we suppose that it is the same 
individual substance which endures, or that it is I who subsist 
during the time AB and am then at Paris, and also I who subsist 
during the time BC and am then in Germany, there must necessarily 



216 THE CONCEPTION OF SUBSTANCE. 

be a reason which makes it true to say that we last, i.e. that I, who 
have been in Paris, am now in Germany. For if there were none, 
we should have just as much right to say that it is another. It is 
true that my internal experience has convinced me d, posteriori of 
this identity, but there must also be an A priori reason. Now it is 
impossible to find any other, except that my attributes of the 
earlier time and state, as well as my attributes of the later 
time and state, are predicates of the same subject, insunt eidem 
subjecto. But what is meant by saying that the predicate is in the 
subject, if not that the notion of the predicate is found in some way 
contained in the notion of the subject? And since, from the 
moment that I began to be, it could be truly said of me that this or 
that would happen to me, we must admit that these predicates were 
laws contained in the subject, or in the complete notion of me, 
which makes what is called /, which is the foundation of the con- 
nection of all my different states, and which God knew perfectly 
from all eternity. After this, I believe, all doubts must disappear, 
for in saying that the individual notion of Adam involves all that 
will ever happen to him, I mean nothing else but what all philo- 
sophers mean when they say that the predicate is in the subject of a 
true proposition. 

G. II. 76 (1686) Substantial unity demands a complete, indi- 
visible, and naturally indestructible being, since its notion involves 
all that is ever to happen to it. 

G. II. 77 (1686). The notion of individual substance in 
general, which I have given, is as clear as that of truth. 

G. II. 457. I'or the nature of an accident, it does not suffice 
that it should be dependent on a substance, for composite substance 
also depends on simple ones or Monads ; but it must be added that 
it depends on a substance as its subject, and moreover as its ulti- 
mate subject ; for an accident may be an aflfection of another 
accident, e.g. magnitude [may be an affection] of heat or of impetus, 
so that the impetus is the subject, and its magnitude inheres in it 
as the abstract of a predicate, when the impetus is said to become 
great, or so great. But the heat or impetus is in a body as its 
subject ; and the ultimate subject is always a substance. 

G. II. 458. I do not see how we can distinguish the abstract 
from the concrete, or from the subject in which it is, or explain 
intelligibly what it is to be or inhere in a subject, unless by con- 
sidering the inherent as a mode or state of the subject. 

G. II. 271. H the principle of action were external to all, 



THE CONCEPTION OF SUBSTANCE. 217 

internal to none, it would be nowhere at all, but we should have 
to recur, with the occasionalists, to God as the sole agent. There- 
fore it is, in truth, internal to all simple substances, since there is 
no reason why it should be in one rather than another ; and it 
consists in the progression of perceptions of each Monad. 



IV. § 18. The meaning of activity. 

G. V. 46 (N. E. 47 ; L. 369). I maintain that, naturally, a 
substance cannot be without action, and indeed that there is never 
a body without motion. 

G. V. 100 (N. E. 110). Faculties without some act, in a word 
the pure powers of the school, are mere fictions, unknown to nature, 
and obtained only by making abstractions. 

G. V. 200 (N. E. 224). If power is taken as the source of 
action, it means something more than an aptitude or facility... for it 
involves tendency also This is why, in this sense, I am accus- 
tomed to apply to it the term enteleehy, which is either primitive, 
and corresponds to the soul taken as something abstract, or deriva- 
tive, such as is conceived in conation, and in vigour and impetu- 
osity. 

Gr. IV. 469 (D. 69). The notion of force or power..., for the 
explanation of which I have designed the special subject of Dy- 
namics, brings very much light for the understanding of the true 
notion of substance. 

G. IV. 479 (D. 73; L. 302). As all shnple substances 
which have a genuine unity can have a beginning and an end only 
by miracle, it follows that they can come into being only by creation 
and come to an end only by annihilation. Thus I was obliged to 
recognize that (with the exception of the souls which God still 
intends specially to create) the constitutive forms of substances 
must have been created with the world and subsist always. 

G. II. 264. "That changes happen," you say, "experience 
teaches ; but we are not inquiring what experience teaches, but 
what follows from the very nature of things." But do you then 
suppose that I am either able or desirous to prove anything in 
nature, unless changes are presupposed? 

G. IV. 507 (D. 115). Since this past decree [by which God 
created the world] does not exist at present, it can produce nothing 
now unless it then left after it some perduring effect, which now 



218 THE CONCEPTION OF SUBSTANCE. 

still continues and operates. And he who thinks otherwise re- 
nounces, if I judge rightly, all distinct explanation of things, and 
will have an equal right to say that anything is the result of any- 
thing, if that which is absent in space or time can, without inter- 
mediary, operate here and now But if, on the contrary, the law 

decreed by God [at the creation] left some trace of itself impressed 
on things; if things were so formed by the mandate as to render 
them fit to accomplish the will of the legislator, then it must be 
admitted that a certain efficacy, form, or force, ...was impressed on 
things, whence proceeded the series of phenomena, according to the 
prescription of the first command. This indwelling force, however, 
may indeed be distinctly conceived, but not explained by images 
{imaginahiliter) ; nor indeed ought it to be so explained, any more 
than the nature of the soul, for force is one of those things which 
are not to be grasped by the imagination, but by the intellect 

G. IV. 508 (D. 117). The very substance of things consists in 
the force of action and passion ; whence it follows that even durable 
things could not be produced at all, unless a foi'ce of some perma- 
nence can be imprinted upon them by the divine power. In that 
case it would follow that no created substance, no soul, would 
remain numerically the same ; that nothing would be preserved 
by God, and consequently that all things would be only certain 
passing and evanescent modifications and apparitions, so to speak, 
of one permanent divine substance. 

G. IV. 509 (D. 117). Another question is whether we must 
say that creatures properly and truly act. This question is included 
in the first, if we once understand that the nature given to them 
does not differ from the force of action and passion. 

G. II. 169. The system of things might have been constituted 
in innumerable ways, but that which had the strongest reason on 
its side prevailed. The activity of substance, however, is rather of 
metaphysical necessity, and would have had a place, if 1 am not 
mistaken, in any system whatever. 



IV. § 19. Connection between activity and sufficient reason. 

G. I. 372 (ca. 1676). This variety of thoughts cannot come 
from what thinks, since a single thing cannot be the cause of the 
changes in itself. For everything remains in the state in which it 
is, if there is nothing to change it ; and not having been determined 
of itself to have certain changes rather than others, we could not 



THE IDENTITY OF INDISCERNIBLES. 219 

begin attributing any variety to it, without saying something for 
which there is confessedly no reason, which is absurd. 

G. II, 263. From universals follow eternal things, from singu- 
lars follow also temporal things, unless you think that temporal 
things have no cause. " Nor do I see," you [De Voider] say, " how 
any succession can follow from the nature of a thing regarded in 
itself." No more it can, if we assume a nature which is not singu- 
lar But all singular things are successive, or subject to 

succession. ...Nor is there, for me, anything permanent in them, 
except the law itself, which involves continued succession, agreeing 
in singulars with that which is in the universe as a whole. 



IV. § 22. Relation of time to Leibniz's notion of substance. 

G. IV. 582. The essential and the natural are always distin- 
guished. ...Properties are essential and eternal, but modifications may 
be natural though changing. 

G. II. 258. I distinguish between properties, which are per- 
petual, and modifications, which are transitory. What follows from 
the nature of a thing may follow perpetually, or for a time. ...From 
the nature of a body moving in a given straight line, with given 
velocity, it follows, if nothing extrinsic be assumed, that after a 
given time has elapsed it will reach a given point in the straight 
line. But will it therefore reach this point always and perpetually ? 

V. § 23. Meaning of the identity of indiscemihles. 

G. VII. 372 (D. 247). Those great principles, of a suflScient 
reason, and of the identity of indiscernibles, change the state of 
metaphysics. That science becomes real and demonstrative by 
means of these principles; whereas before it did generally consist 
in empty words. 

G. V. 100 (N. E. 110). According to the proofs which I 
believe I possess, every substantial thing, whether soul or body, has 
its own proper relation to each of the others ; and one must always 
diflfer from the other by intrinsic denominations. 

G. VII. 393 (D. 258). I infer from that principle [of suflacient 
reason], among other consequences, that there are not in nature two 
real, absolute beings, indiscernible from each other ; because if there 
were, God and nature would act without reason, in ordering the one 
otherwise than the other. 



220 THE IDENTITY OF INDISCERNIBLES. 

G. VII. 407 (D. 273). God... will never choose among indis- 
cernibles. 

G. V. 213 (N. E. 238). It is always necessary that, besides 
the difference of time and place, there should be an internal prin- 
ciple of distinction, and though there be several things of the same 
species, it is none the less true that there are none perfectly similar : 
thus, though time and place {i.e. relation to the external) help us to 
distinguish things which by themselves we do not well distinguish, 
things are none the less distinguishable in themselves. Thus the 
essence {le precis) of identity and diversity consists not in time and 
place, though it is true that the diversity of things is accompanied 
by that of time and place, because they bring with them different 
impressions on the thing. 

G. II. 131. Can it be denied that everything (whether genus, 
species or individual) has a complete notion, according to which it 
is conceived by God, who conceives everything perfectly — i.e. a 
notion containing or comprehending all that can be said about the 
thing : and can it be denied that God can form such an individual 
notion of Adam or Alexander, which comprehends all the attributes, 
affections, accidents, and generally all the predicates of this subject. 

G. II. 249. Things whicli are different must differ in some 
way, or have in themselves some assignable diversity ; and it is 
wonderful that this most manifest axiom has not been employed by 
men along with so many others. 

V. § 25. 7s Leibniz's proof of the principle valid ? 

G. V. 202 (N. E. 225). We know that it is abstractions which 
give rise, when we wish to scrutinize them, to the greatest number 

of difficulties, of which the thorniest fall at once if we agree to 

banish abstract beings, and resolve to speak ordinarily only in con- 
cretes, admitting no other terms in the demonstrations of science but 

such as represent substantial subjects When we distinguish two 

things in substance, the attributes or predicates and the common 
subject of these predicates, it is no wonder if nothing particular can 
be conceived in this subject. This is necessary, since we have already 
separated all the attributes, in which we could conceive some detail. 
Thus to demand, in this pure subject in general, anything beyond 
what is required to conceive that it is the same thing {e.g. which 
understands and wills, imagines and reasons), is to demand the 
impossible, and to contravene our own supposition, which we made 



THE IDENTITY OF INDISCERNIBLES. 221 

in abstracting and conceiving separately the subject and its quali- 
ties or accidents. 



V. § 26. Every substance has an infinite number of predi- 
cates. Connection of this with contingency and with the 
identity of indiscernibles. 

G. III. 582. There is a. difference between analysis of the 
necessary and analysis of the contingent : the analysis of the neces- 
sary, which is that of essences, going from the posterior by nature 
to the prior by nature, ends in primitive notions, and it is thus that 
numbers are resolved into units. But in contingents or existents, 
this analysis from the subsequent by nature to the prior by nature 
goes to infinity, without a reduction to primitive elements being 
ever possible. 

G. V. 268 (N, £. 309). Paradoxical as it appears, it is impos- 
sible for us to have knowledge of individuals, and to find the means 
of determining exactly the individuality of any thing, unless we 
keep it [the thing?] itself; for all the circumstances may recur; the 
smallest difl^erences are insensible to us _: the place and the time, far 
from determining [things] of themselves, need to be themselves 
determined by the things they contain. What is most noteworthy 
in this is, that individuality involves infinity, and only he who is 
capable of understanding it [infinity] can have knowledge of the 
principle of individuation of such or such a thing; which comes 
from the influence (rightly understood) of all the things in the 
universe on one another. It is true that the matter would be other- 
wise if there were atoms of Democritus ; but also there would then 
be no difference between two different individuals of the same shape 
and size. 

P. de C. 24 (D. 175). Individuals cannot be distinctly con- 
ceived. B[ence they have no necessary connection with God, but 
are produced freely. 

Cr. VII. 309. It is essential to discriminate between necessary 
or eternal truths, and contingent truths or truths of fact ; and these 
differ from each other almost as rational numbers and surds. For 
necessary truths can be resolved into such as are identical, as com- 
mensurable quantities can be brought to a common measure; but 
in contingent truths, as in surd numbers, the resolution proceeds to 
infinity without ever terminating. And thus the certainty and the 
perfect reason of contingent truths is known to God only, who 



222 THE LAW OF CONTINUITY. 

embraces the infinite in one intuition. And when this secret is 
known, the difficulty as to the absolute necessity of all things is 
removed, and it appec'irs what the difierence is between the infallible 
and the necessary. 

Gr. VII. 200. Any truth which is incapable of analysis, and 
cannot be proved from its reasons, but takes its ultimate reason and 
its certainty from the divine mind alone, is not necessary. And 
such are all those that I call truths of fact. And this is the source 
of contingency, which no one, to my knowledge, has hitherto 
explained. 

V. § 27. The Law of Continuity: three forms of continuity 
maintained by Leibniz. 

Gt. V. 49 (N. E. 50 ; L. 376). Nothing happens all at once, 
and it is one of my great maxims, and among the most completely 
verified, that nature never makes leaps : which I called the Law of 

Continuity I have remarked also that, in virtue of insensible 

variations, two individual things cannot be perfectly similar, and 
must always differ more than numerically. 

Gt. V. 455 (N. E. 552). Everything goes by degrees in nature, 
and nothing by leaps, and this rule as regards changes is part of my 
law of continuity. But the beauty of nature, which desires distin- 
guished perceptions, demands the appearance of leaps. 

G. III. 52 (D. 33), A principle of general order which 

I have noticed... is of great utility in reasoning It takes its origin 

from the infinite, it is absolutely necessary in Geometry, but it 
succeeds also in Physics, because the sovereign wisdom, which is the 
source of all things, acts as a perfect geometer, following a harmony 
to which nothing can be added. ...It [the principle] may be enun- 
ciated thus : " When the difference of two cases can be diminished 
below every given magnitude in the data or in what is posited, it 
must also be possible to diminish it below every given magnitude in 
what is sought or in what results," or, to speak more familiarly, 
" When the cases (or what is given) continually approach and are 
finally merged in each other, the consequences or events (or what is 
sought) must do so too." Which depends again on a still more 
general principle, namely : " When the data form a series, so do the 
consequences " (datis ordinatis etiam quaesita sunt ordinata). 

G. II. 168. No transition happens by a leap. ...This holds, I 
think, not only of transitions from place to place, but also of those 



POSSIBILITY AND COMPOSSIBILITY. 223 

from form to form, or from state to state. Tor not only does ex- 
perience confute all sudden changes, but also I do not think any 
d, priori reason can be given against a leap from place to place, 
which would not militate also against a leap from state to state. 

G. II. 182. Assuming that everything is always created by 
God, nothing prohibits a body, if we depart from the laws of order, 
from being transcreated by a leap from place to place, so that it 
jumps in one moment, and then all at once remains at rest for a 
while. A leap, a hiatus, a vacuum, and rest, are condemned by 
the same law. 

G. II. 193. This hypothesis of leaps cannot be refuted, except 
by the principle of order, by the help of the supreme reason, which 
does everything in the most perfect way. 

G. V. 473 (N. E. 575). I conceive things unknown or con- 
fusedly known only after the manner of those which we know 
distinctly ; which renders philosophy very easy, and I even believe 
that we must do so. ..This is why I believe that there is no genius, 
however sublime, but has an infinity of others above him. 



V. § 29. Possibility and Gompossibility. 

G. V. 286 (N. E. 334). I have reasons for believing that not 
all possible species are compossible in the universe, great as it is, 
and that this holds not only in respect to the things which exist 
together at one time, but even in relation to the whole series of 
things. That is, I believe that there necessarily are species which 
never have existed and never will exist, not being compatible with 
that series of creatures which God has chosen The law of con- 
tinuity states that Nature leaves no gap in the order which she 
follows ; but not every form or species belongs to every order. 

G. III. 573. The Universe is only the collection of a certain 
kind of compossibles ; and the actual Universe is the collection of 
all existent possibles, i.e. of those which form the richest compound. 
And as there are different combinations of possibles, some better 
than others, there are many possible Universes, each collection of 
compossibles making one of them. 

V. § 31. The three kinds of necessity. 

G. III. 400 (D. 170). The whole universe might have been 
made differently ; time, space, and matter being absolutely, in- 



224 WHY DID LEIBNIZ BELIEVE IN AN EXTERNAL WORLD? 

different to motions and figures ; and God has chosen among an 
infinity of possibles what he judged to be the most suitable. But 
as soon as he has chosen, it must be admitted that everything is 
comprised in his choice, and that nothing can be changed, since he 
foresaw and arranged everything once for all. ...It is this necessity, 
which can be attributed now to things in the future, which is called 

hypothetical or consequential But though all the facts of the 

universe are now certain in relation to God, ...it does not follow 
that their connection is always truly necessary, i.e. that the 
truth, which pronounces that one fact follows from another, is 
necessary. 

G. VII. 389 (D. 255). We must distinguish between an abso- 
lute and an hypothetical necessity. We must also distinguish 
between a necessity which takes place because the opposite implies 
a contradiction (which necessity is called logical, metaphysical, or 
mathematical), and a necessity which is moral, whereby a wise 
being chooses the best, and every mind follows the strongest incli- 
nation. 



VI. § 33. The existence of the external world has only 
" moral certainty." 

G. I. 372 (cos. 1676). This variety of thoughts cannot come 
from what thinks, since a thing cannot itself be the cause of its own 

changes Therefore there is outside of us some cause of the variety 

of our thoughts. And since we agree that there are certain sub- 
ordinate causes of this variety, which nevertheless themselves need 
causes, we have established particular beings or substances in which 
we recognize some action, i.e. of which we conceive that from their 
change follows some change in ourselves. And we are marching 
with great strides towards the construction of what we call matter 
and body. But it is at this point that you [Foucher] are right in 
delaying us a little, and renewing the complaints of the ancient 
Academy. For all our experiences, at bottom, assure us of only 
two things, namely, that there is a connection between our appear- 
ances which gives us the means of successfully predicting future 
appearances, and that this connection must have a constant cause. 
But from all this it does not follow, strictly speaking, that matter 
or bodies exist, but only that there is something which presents 
well-ordered appearances to us. For if an invisible power took 
pleasure in making dreams, well connected with our previous life 



WHY DID LEIBNIZ BELIEVE IN AN EXTERNAL WORLD? 225 

and agreeing with each other, appear to us, should we be able to 
distinguish them from realities until we had been awakened? Or 
what prevents the whole course of our life from being a great orderly 
dream, of which we might be disillusioned in a moment ? And I 
do not see that this Power would for that reason be imperfect, as 
M. Des Cartes assures, besides that its imperfection does not enter 
into the question. 

G. V. 275 (N. E. 318). God has ideas (of substances) before 
creating the objects of these ideas, and nothing prevents him from 
also communicating such ideas to intelligent creatures ; there is not 
even any exact demonstration proving that the objects of our senses, 
and of the simple ideas which our senses present to us, are outside 
of us. 

G. V. 355 (N. E, 422). I believe the true criterion as regards 
objects of sense is the connection of phenomena, i.e. the connection 
of what happens in different times and places, and in the experience 
of different men, who are themselves, in this respect, very important 

phenomena to one another But it must be confessed that all this 

certainty is not of the highest degree. ...For it is not impossible, 
metaphysically speaking, that there should be a dream as connected 
and lasting as the life of a man ; but it is a thing as contrary to 
reason as would be the fiction of a book produced by chance in 
throwing the printer's types pell-mell. 

G. VII. 320 (N. E. 719). It cannot be absolutely demon- 
strated, by any argument, that there are bodies, and nothing 
prevents some well-ordered dreams from being offered to our minds, 
which would be judged by us to be true. ..Nor is the argument of 
great weight, which is commonly adduced, that thus God would 
be a deceiver ; undoubtedly no one fails to see how far this is from 
a demonstration giving metaphysical certainty, since, in asserting 
something without accurate investigation, we should be deceived 
not by God, but by our own judgment. 

G. V. 205 (N. E. 229). It is very true that the existence of 
spirit is more certain than that of sensible objects. 

G. II. 516. From the reason of things we judge (even without 
respect to the divine wisdom) that we do not exist alone, since there 
appears no reason of a privilege in favour of one. Nor will you be 
able otherwise to convince by reason any one who contends that he 
alone exists, and that others are merely dreamed by him. But 
there is a reason for the privilege of existents over non-existents, or 
why not all possibles exist. Moreover even if no creatures existed 

E. L. 15 



226 THE PHILOSOPHY OF DYNAMICS. 

except the percipient, the order of perceptions would show the 
divine wisdom. Thus there is no circle here, although the wisdom 
of God is also derived d, priori, and not only from the order of 
phenomena. For from the mere fact that there are contingents it 
follows that there is a necessary Being. 

VII. § 35. Various meanings of matter and body. 

G. III. 657 (D. 234). Primary and pure matter, taken without 
the souls or lives which are united to it, is purely passive; also, 
properly speaking, it is not a substance, but something incomplete. 
And secondary matter {e.g. an organic body) is not a substance, but 
for another reason, namely, that it is a collection (amas) of several 
substances, like a pond full of fish, or a flock of sheep, and con- 
sequently it is what is called unum per accidens — in a word, a 
phenomenon. A true substance (such as an animal) is composed of 
an immaterial soul and an organic body, and it is the compound of 
these two which is called unum per se. 

G. VII. 501 (N. E. 722). Matter is what consists in Antitypia, 
or what resists penetration ; and thus bare matter is merely passive. 
But body has, besides matter, active force also. Now body is either 
corporeal substance, or a mass composed of corporeal substances. I 
call corporeal substance what consists in a simple substance or monad 
(i.e. a soul or something analogous to a soul) and an organic body 
united with it. But mass is the aggregate of corporeal substances, 
as cheese sometimes consists of a concourse of worms. 

G. II. 252, I distinguish (1) the primitive entelechy or soul, 
(2) primary matter or primitive passive power, (3) the monad, com- 
pleted by these two, (4) mass or secondary matter or the organic 
machine, to which innumerable subordinate monads concur, (5) the 
animal, or corporeal substance, which is made into one machine by 
the dominant monad. 

VII. § 36. Relation of Leibnizian and Cartesian Dynamics. 

G. IV. 497 (D. 88). You know that M. Des Cartes believed 
that the same quantity of motion is preserved in bodies. It has 
been shown that he was mistaken in this ; but I have shown 
that it is always true that the same motive force is preserved, for 
which he had taken the quantity of motion. However the changes 
which happen in bodies in consequence of modifications of the soul 
embarrassed him, because they seemed to violate this law. He 



THE PHILOSOPHY OF DYNAMICS. 227 

believed, therefore, that he had found an expedient, which is 
certainly ingenious, by saying that we must distinguish between 
motion and direction ; and that the soul cannot augment or diminish 
the moving force, but alters the direction, or determination of the 
course of the animal spirits, and that it is through this that voluntary 

motions take place But it must be known that there is another 

law of nature, which I have discovered and proved, and which M. 
Des Cartes did not know : this is that not only the quantity of 
moving force is conserved, but also the same quantity of direction 
[momentum] towards whichever part it may be taken in the world. . . . 
This law, being as beautiful and general as the other, was also 
worthy of not being violated : and this is what my system effects, 
by conserving force and direction, and in a word all the natural 
laws of bodies, notwithstanding the changes which happen in them 
in consequence of those of the soul. 

G. VI. 540 (D. 164). If people had known, at the time of 
M. Des Cartes, that new law of nature, which I have proved, 
which asserts that not only the total force of bodies that have 
connection with each other is conserved, but also their total direction, 
he would apparently have come to my System of the pre-established 
Harmony. 

Or. IV. .286 (D. 5) (1680). The Physics of M. Des Cartes has 
a great defect ; this is that his rules of motion, or laws of nature, 
which are intended to be the foundation, are for the most part 
false. There is proof of this : and his great principle, that the same 
quantity of motion is conserved in the world, is a mistake. "What 
I say here is recognized by the ablest people in France and England. 



VII. § 37. The essence of matter is not esctension. 

G. I. 58 (ca. 1672). In natural philosophy I am perhaps the 
first to have proved thoroughly... that there is a vacuum. [It follows 
that the essence of matter is not extension.] 

G. II. 71 (1686). [Assuming that bodies are substances] it can 
be inferred that corporeal substance does not consist of extension or 
divisibility ; for it will be admitted that two bodies remote one from 
another, e.g. two triangles, are not really one substance ; let us 
suppose now that they approach so as to make a square ; will mere 
contact make them into one substance ? I think not. Now every 
extended mass can be considered as composed of two or a thousand 
others ; we have merely extension by contact. Thus we shall never 

15—2 



228 THE PHILOSOPHY OF DYNAMICS. 

find a body of which we can say that it is truly one substance. It 
will be always an aggregate of many. Or rather it will not be a 
real being, because the parts which compose it are subject to the 
same difficulty. ...But also the general notion of individual sub- 
stance... proves the same thing. Extension is an attribute which 
cannot constitute a complete being, no action or change can be 
derived from it, it expresses merely the present state, but not at 
all the future or the past, as the notion of a substance should. 
When two triangles are joined, we cannot from this conclude how 
the junction came about. 

G. III. 97. We cannot conceive that resistance should be a 
modification of extension. 

G. III. 453. Impenetrability is not a consequence of extension; 
it presupposes something more. Place is extended, but not im- 
penetrable. 

G. II. 233. Yon admit that existence and continuity, which 
are constituents of the notion of extension, difi'er formally, and I 
demand no more ; but in truth that of which the notion is formed 
of different formal concepts, is not primitive. It is one of the 
primary errors of the Cartesians that they conceived extension as 
something primitive and absolute, and as what constitutes substance. 

G. II. 169. I do not think that extension alone can constitute 
a substance, since the notion of extension is incomplete ; and I hold 
that extension cannot be conceived per se, but is a resolvable and 
relative notion ; for it is resolved into plurality, continuity, and 
coexistence or the existence of parts at one and the same time. 
Plurality is also contained in number, continuity also in time and 
motion, while coexistence is only added in extension. 



VII. § 38. Meaning of materia prima in Leibniz's Dynamics. 

G. II. 171. The resistance of matter contains two things, 
impenetrability or antitypia, and resistance or inertia ; and in these, 
since they are everywhere equal in a body, or proportional to its 
extension, I place the nature of the passive principle or matter ; as, 
in active force, displaying itself variously in motions, I recognize the 
primitive entelechy, or so to speak something analogous to a soul, 
whose nature consists in a perpetual law of its series of changes, 
which it describes uninterruptedly. 

G. II. 170. I observed that Des Cartes in his letters, following 
the example of Kepler, had recognized inertia everywhere in matter. 



THE PHILOSOPHY OF DYNAMICS. 229 

This you [de Voider] deduce from the force which anything has of 
remaining in its (present) state, which force does not diflfer from its 
own nature. Thus you judge that the simple concept of extension 
suffices even for this phenomenon. ...But it is one thing to retain the 
actual state until there is something which changes it, which is done 
even by what is in itself indifferent to either, while it is something 
other and much more that a thing should not be indifferent, but 
have a force, and as it were an inclination, to retain its state and 

should resist the cause of change And a world can be imagined, as 

at least possible, in which matter at rest would obey a cause of motion 
without any resistance ; but such a world would be a mere chaos. 

G. V. 206 (N. E. 231). I believe that perfect fluidity belongs 
only to materia prima, i.e. in abstraction, and as an original quality, 
like rest; but not to materia secunda, such as it actually occurs, 
invested with its derivative qualities. 

G. V. 325 (N. E. 383). It is not so useless as is supposed to 
reason about materia prima in general Physics, and to determine its 
nature, so as to know whether it is always uniform, whether it has 
any other property besides impenetrability (as in fact I have shown, 
after Kepler, that it has also what may be called inertia) etc., though 
it never occurs quite bare. 

G. IV. 393 (N. E. 699). There is in body something passive 
besides extension, that namely by which a body resists penetration. 

G. IV. 395 (N. E. 701). ™ Wa/itKov or power in body is 
twofold, passive and active. Passive force properly constitutes matter 
or mass, active force constitutes ivTiXexn-a-v or form. Passive force 
is that resistance by which a body resists not only penetration, but 
also motion, and in virtue of which another body cannot come into 
its place unless it gives way, while it does not give way except by 
somewhat retarding the motion of the impelling body, and thus tries 
to persevere in its former state.... Thus there are in it two resistances 
or masses : the first is called antitypia or impenetrability, the second, 
resistance, or what Kepler calls the natural inertia of bodies. 

G, VII. 328. I call antitjrpia that attribute in virtue of which 
matter is in space. ...The modification or variety of antitypia consists 
in the variety of place. 



VII. § 39. Materia secunda. 

G. M. VI. 235 (N. E. 671). There is in corporeal things 
something besides extension, nay prior to extension, namely the very 



230 THE PHILOSOPHY OF DYNAMICS. 

force of nature everywhere implanted by its Author, which consists, 
not in the simple faculty with which the schools seem to have been 
content, but is provided, besides, with a conation or effort which 
will have its full effect unless impeded by a contrary conation. 

G. IV, 470 (D. 70). Corporeal substance never ceases to act, 
any more than does spiritual substance. 

G. M. VI. 237 (N. E. 673). Because of form, every body 
always acts ; and because of matter, every body always endures and 
resists. 

G. IV. 513 (D. 122). Not only is a body at the present 
moment of its motion in a place commensurate to it, but it has also 
a conation or effort to change its place, so that the succeeding state 
follows of itself from the present state by the force of nature ; other- 
wise in the present, and also in any moment, a body A which is in 
motion would differ in no way from a body B which is at rest. 

G. IV. 396 (N. E. 702). Many things compel us to place 
active force in bodies, especially that experience which shows that 
there are motions in matter, which, though they are attributable 
originally to the general cause of things, God, yet are immediately 
and specially attributable to the force placed by God in things. 
For it is nothing to say that God in creation gave bodies a law of 
action, unless he gave them, at the same time, something by which 
the law was to be observed ; otherwise he himself would always 
have to procure the observation of the law by extraordinary means. 

G. III. 60. There is always conserved in the world the same 
quantity of motor action, i e. rightly understood, there is as much 
motor action in the universe in one hour as in any other hour what- 
ever. But in moments themselves it is the same quantity of force 
which is conserved. And in fact action is nothing but the exercise 
of force, and amounts to the product of the force and the time. 

G. IV. 610 (D. 119). That bodies are of themselves inert 
is true if it be rightly understood, to this extent namely, that 
what is, for some reason, once assumed to be at rest cannot 
set itself in motion, and does not allow itself without resistance 
to be set in motion by another body ; any more than it can of 
itself change the degree of velocity or the direction which it once 
has, or allow it easily and without resistance to be changed by 
another body. And also it must be confessed that extension, or 
what is geometrical in body, if taken simply, has nothing in it 
which can give rise to action and motion ; on the contrary, matter 
rather resists motion by a certain natural inertia, as Kepler has well 



THE PHILOSOPHY OF DYNAMICS. 231 

called it, so that it is not indifferent to motion and rest, as is 
generally supposed, but needs, in order to move, an active force 
proportional to its size. Wherefore I make the very notion of 
materia prima, or of mass, which is always the same in a body and 
proportional to its size, consist of this very passive force of re- 
sistance (involving both impenetrability and something more) ; and 
hence I show that entirely different laws of motion follow than 
if there were in body and in matter itself only impenetrability 
together with extension ; and that, as there is in matter a natural 
inertia opposed to motion, so in body, and what is more in every 
substance, there is a natural constancy opposed to change. But 
this doctrine does not defend, but rather opposes, those who deny 
action to things ; for just as certain as it is that matter of itself 
does not begin motion, so certain is it (as is shown by excellent 
experiments on the motion communicated by a moving body) that 
a body retains of itself the impetus which it has once acquired, and 
that it is stable in its levity, or makes an effort to persevere in 
that very series of changes upon which it has entered. As these 
activities and entelechies cannot be modifications of primary matter 
or mass, a thing essentially passive,... it may be hence inferred that 
there must be found in corporeal substance a first entelechy or 
irptoTov SeKTtKov for activity; i.e. a primitive motor force which, 
joined to extension (or what is purely geometrical) and to mass 
(or what is purely material) always indeed acts, but nevertheless, 
in consequence of the meeting of bodies, is variously modified 
through efforts and impetus. And it is this same substantial 
principle which is called soul in living beings, and substantial 
form in others. 

VII. § 41. Force and absolute motion. 

G. IV. 400 (N. E. 706). If forces are taken away, motion 
itself has nothing real left in it, for from the mere variation of 
position we cannot tell where the true motion or cause of variation is. 

G. II. 137 (D. 39). As regards Physics, we must understand 
the nature of force, a thing quite different from motion, which is 
something more relative. 

G. IV. 369 (D. 60). If motion is nothing but change of 
contact or immediate vicinity, it will follow that we can never 

determine which thing is moving Thus if there is nothing in 

motion but this relative change, it follows that there is no 



232 THE PHILOSOPHY OF DYNAMICS. 

reason in nature for ascribing motion to one thing rather than 
others. The consequence of which will be, that there is no real 
motion. Thus in order to say that anything moves, we require 
not only that it should change its situation relatively to other 
things, but also that it should contain the cause of change, the 
force or action. 

G. VII. 403 (D. 269). Motion does not depend upon being 
observed, but it does depend upon being possible to be observed. 
...When there is no change that can be observed, there is no 

change at all I find nothing in the eighth definition of the 

Mathematical Principles of Nature, nor in the scholium belonging 
to it, that proves, or can prove, the reality of space in itself. How- 
ever, I grant there is a difierence between an absolute true motion 
of a body, and a mere relative change of its situation with respect 
to another body. For when the immediate cause of the motion is in 
the body, that body is truly in motion. 

G. M. II. 184. -A-S for the difierence between absolute and 
relative motion, I believe that if motion, or rather the moving 
force of bodies, is something real, as it seems we must recognize, it 
is necessary that it should have a subject. .. .You [Huygens] will not 
deny, I believe, that really each [body in impact] has a certain 
degree of motion, or if you will, of force, notwithstanding the equi- 
valence of hypotheses. It is true, I derive hence the consequence 
that there is in bodies something other than Geometry can determine 
in them. And this is not the least among several reasons which I 
use to prove that, besides extension and its variations (which are 
something purely geometrical), we must recognize something superior, 
which is force. Mr Newton recognizes the equivalence of hypotheses 
in the case of rectilinear motions ; but as regards circular motions, 
he believes that the eflbrt which revolving bodies make, to recede 
from the centre or axis of revolution, makes known their absolute 
motion. But I have reasons which make me believe that nothing 
breaks the general law of equivalence. 

G. II. 91 (1687). What is real in the state called motion 
proceeds just as much from corporeal substance as thought and will 
proceed from the mind. 

G. II. 115 (1687). A corporeal substance gives itself its own 
motion, or rather what is real in the motion at each instant, i.e. the 
derivative force, of which it is a consequence; for every present 

state of a substance is a consequence of its preceding state If God 

ever reduces a body to perfect rest, which could only be done by 



THE PHILOSOPHY OF DYNAMICS. 233 

miracle, a new miracle will be required to restore any motion to 
it. 

G. IV. 486 (D. 80; L. 318). As to absolute motion, nothing 
can determine it mathematically, since all ends in relations, with the 
result that there is always a perfect equivalence of hypotheses, as in 
Astronomy.... Yet it is reasonable to attribute to bodies real motions, 
according to the supposition which explains the phenomena in the 
most intelligible way, for this denomination is in harmony with 
the notion of activity. 

G. V. 370 (N. E. 440). The infinitesimal analysis has given 
us the means of allying Geometry with Physics. 

G. M. VI. 247 (N. E. 684). It must be known, to begin with, 
that force is indeed something truly real, even in created substances; 
but space, time and motion are of the nature of rational entities, 
and are true and real, not of themselves, but in so far as they involve 
divine attributes — immensity, eternity, operation — or the force of 
created substances. Hence it follows at once that there is no 
vacuum in space or time; that motion, moreover, apart from force,... 
is in truth nothing else than a change of situation, and thus motion, 

as far as phenomena a/re concerned, consists in a mere relation It 

follows also, from the relative nature of motion, that the action of 
bodies on each other, or impact, is the same, provided they approach 

each other with the same velocity Meanwhile we speak as the 

matter requires, for a more suitable and simpler explanation of the 
phenomena, precisely as... in the theory of the planets we must use 
the Copernican hypothesis — For although force is something real 
and absolute, nevertheless motion pertains to the class of relative 
phenomena, and truth is looked for not so much in phenomena as in 
causes. 



VII. § 42. Metaphysical grounds for assuming force. 

G. III. 45. There is always a perfect equation between the 
complete cause and the whole effect. ...Though this axiom is wholly 
metaphysical, it is none the less one of the most useful that can 
be employed in Physics. 

G. III. 48. I have shown that force must not be estimated 
by the compound of velocity and size, but by the future effect. 
However it seems that force or power is something already real, 
while the future effect is not so. Whence it follows that we must 



234 THE PHILOSOPHY OF DYNAMICS. 

admit in bodies something different from size and velocity, unless 
we are willing to refuse to bodies all power of acting. 

G. M. VI. 252 (N. E. 689). Since only force, and the effort 
which arises from it, exists at any moment (for motion never truly 
exists...), and every effort tends in a straight line, it follows that 
all motion is rectilinear, or composed of rectilinears. 

G. VII. 305 (D. 103 ; L. 344). Metaphysical laws of cause, 
power, activity, are present in a wonderful way throughout the 
whole of nature, and are even superior to the purely geometrical 
laws of matter. 

G. IV. 523. As for motion, what is real in it is force or 
power, i.e. what there is in the present state that brings with it a 
change for the future. The rest is only phenomena and relations. 

VII. § 43. Bynamical argument for plurality of causal 

series. 

G. V. 158 (N. E. 176). Though it is not true that a body [in 
impact] loses as much motion as it gives, it is always true that it 
loses some motion, and that it loses as much force as it gives. 

G. M. VI. 251 (N. E. 688). The passion of every body is 
spontaneous, or arises from an internal force, though upon occasion 
of something external. 

G. M. VI. 252 (N. E. 689) (1695). The action of bodies is 
never without reaction, and both are equal to each other and directly 
contrary. 

G. M. VI. 230. This diminution of the total force [in a not 
perfectly elastic impact]... does not derogate from the inviolable 
truth of the conservation of the same force in the world. For what 
is absorbed by the small parts is not absolutely lost to the universe, 
though it is lost for the total force of the impinging bodies. 

VII. § 45. His grounds against extended atoms. 

G. I. 403. My axiom, that nature never acts by leaps, ...is of 
the greatest use in Physics ; it destroys a;toms, intervals of rest 
[quietulas], globes of the second element, and other similar chimeras. 

G. M. II. 136. I confess that I have diflSculty in understanding 
the reason of such infrangibility [as that of atoms], and I believe 
that for this effect we should have to have recourse to a kind of 
perpetual miracle. 

G. M. II. 145. There is no absurdity in giving different 



THE PHILOSOPHY OF DYNAMICS. 235 

degrees of rigidity to different bodies ; otherwise we could prove by 
the same reason that bodies must have a zero or an infinite velocity. 
...There are other inconveniences about atoms. For example, they 
could not be susceptible of the laws of motion, and the force of two 
equal atoms, which impinged directly with equal velocities, would 
have to be lost ; for it seems that only elasticity makes bodies 
rebound. 

G. M. II. 156. Matter, according to my hypothesis, would be 
divisible everywhere and more or less easily with a variation which 
would be insensible in passing from one place to another neighbour- 
ing place ; whereas, according to the atoms, we make a leap from 
one extreme to the other, and from a perfect incohesion, which is in 
the place of contact, we pass to an infinite hardness in all other 
places. And these leaps are without example in nature. 

Gr. M. II. 157. There is no last little body, and I conceive that 
a particle of matter, however small, is like a whole world, full of 
an infinity of still smaller creatures. 

VII. § 46. Against the vacuum. 

Gr, II, 475. The infinity of the physical continuum, in. the 
hypothesis that there are only monads, does not depend so much 
on the reason of the best, as on the principle of sufficient reason, 
because there is no reason for limiting or ending, or for stopping 
anywhere. 

G. V. 52 (N. E. 53 ; L. 385). We [Locke and Leibniz] seem 
also to differ as regards matter in this, that the author thinks there 
must be a vacuum in it for the sake of motion, because he believes 
that the small parts of matter are rigid. And I admit that if 
matter were composed of such parts, motion in the plenum would be 
impossible. ...But this supposition is not by any means granted.... 
Space must rather be conceived as full of an ultimately fluid matter, 
susceptible of all divisions, and even subjected actually to divisions 

and subdivisions ad infinitum Consequeiitly matter has everywhere 

some degree of rigidity as well as of fluidity. 

G. IV. 395 (N. E. 701). Although some bodies appear denser 
than others, yet this happens because their pores are more filled 
with matter pertaining to the body, while on the contrary the rarer 
bodies have the nature of a sponge, so that another subtler matter 
washes through their pores, which is not reckoned with the body, 
and neither follows nor awaits its motion. 



236 THE PHILOSOPHY OF DYNAMICS. 

G. IV. 368 (D. 59). Not a few of those who defend a vacuum 
hold space to be a substance, nor can they be refuted by Cartesian 
arguments; there is need of other principles for ending this con- 
troversy. 

G. VII. 356 {D. 240). The more matter there is, the more 
God has occasion to exercise his wisdom and power. Which is one 
reason, among others, why I maintain that there is no vacuum 
at all. 

G. VII. 372 (D. 248). The same reason which shows that 
extramundane space is imaginary, proves that all empty space is an 
imaginary thing ; for they differ only as greater and less. If space 
is a property or attribute, it must be the property of some substance. 
But what substance will that bounded empty space be an affection 
or property of, which its patrons [Clarke and Newton] suppose to 
be between two bodies?... Extension must be the affection of some- 
thing extended. But if that space be empty, it will be an attribute 
without a subject, an extension without anything extended. 

G, VII. 377 (D. 253). All those who maintain a vacuum are 
more influenced by imagination than by reason. When I was a 
young man, I also gave in to the notion of a vacuum and atoms ; 

but reason brought me into the right way I lay it down as a 

principle, that every perfection, which God could impart to things 
without derogating from their other perfections, has actually been 
imparted to them. Now let us fancy a space wholly empty. God 
could have placed some matter in it, without derogating in any 
respect from all other things : therefore he has actually placed some 
matter in that space : therefore there is no space wholly empty : 
therefore all is full. 

G. VII. 396 (D. 261). Absolutely speaking, it appears that 
God can make the material universe finite in extension ; but the 
contrary appears more agreeable to his wisdom. 



VII. § 47. Against action at a distance. 

G. III. 580. We disapprove the method of those [Newton and his 
followers] who suppose, hke the scholastics formerly, unreasonable 
qualities, i.e. primitive qualities which have no natural reason, explic- 
able by the nature of the subject to which this quality is to belong 

As we maintain that it [attraction] can only happen in an explicable 
manner, i.e. by an impulsion of subtler bodies, we cannot admit that 
attraction is a primitive quality essential to matter According to 



THE PHILOSOPHY OF DYNAMICS. 237 

these authors, not only are substances entirely unknown to us, . . .but 
it is even impossible for any one to know them ; and God himself, 
if their nature be such as they say, would know nothing of them. 

G. II. 399. If Grod caused anything to act immediately at a 
distance, he would by that very fact give it multipresence. 

G. II. 407. I reject the natural action of a body at a distance, 
but not the supernatural. 

YII. § 48. Force as conferring individuality. 

G. II. 116. Bodies, strictly speaking, are not pushed by others 
when there is an impact, but by their own motion, or by their 
elasticity (ressort), which again is a motion of their parts. Every 
corporeal mass, great or small, has already in it all the force which 
it can ever acquire, but the meeting with other bodies only gives its 
determination, or rather this determination only happens during the 
time of the meeting. 

VII. § 49. Primitive and derivative force. 

G. II. 262. Derivative force is the actual present state while 
tending to or pre-involving the following state, as everything present 
is big with the future. But that which persists, in so far as it 
involves all that can happen to it, has primitive force, so that 
primitive force is, as it were, the law of the series, while derivative 
force is the determination which designates a particular term of the 
series. 

G. M. VI. 238 (N. E. 674). Force is twofold: the one 
elementary, which I also call dead, because motion does not yet 
exist in it, but only a solicitation to motion...; the other, however, 
is ordinary force, combined with actual motion, which I call living. 

G. III. 457. There are two sorts of force in a body, the one 
primitive, which is essential to it (€i'TeX£;^£ta ij irpwrri), and derivative 
forces, which depend upon other bodies also. And it should be 
considered that the derivative or accidental force, which one cannot 
refuse to bodies in motion, must be a modification of the primitive 
force, as shape is a modification of extension. Accidental forces 
could not occur in a substance without essential force, for accidents 
are only modifications or limitations, and cannot contain more per- 
fection or reality than the substance. 

G. IV. 396 (N. E. 702). Derivative force is what some call 



238 THE PHILOSOPHY OF DYNAMICS. 

impetus, a conation or tendency, so to speak, to some determi- 
nate motion, by which primitive force or the principle of action is 
modified. I have shown that this is not preserved constant in the 
same body, but yet, however it be distributed among many, its sum 
remains constant, and that it differs from motion, whose quantity 
is not conserved. 

G. IV. 533. In the soul, representations of causes are causes 
of representations of effects. 

G. III. 636. As for the inertia of matter, as matter itself is 
nothing but a phenomenon, though well founded, resulting from 
monads, the same holds of inertia, which is a property of this 
phenomenon. 

G. II. 92 (1687). Motions being real phenomena rather than 
beings, one motion as phenomenon is in my mind the immediate 
consequence or effect of another phenomenon, and similarly in the 
minds of others, but the state of one substance is not the immediate 
consequence of the state of another particular substance. 

G. III. 623. The laws of motion, being founded in the percep- 
tions of simple substances, come from final causes or causes due to 
fitness, which are immaterial and in each monad. 

G. II. 419. The entelechy acts in matter according to the need 
of matter, so that the new state of matter is a consequence of the 
prior state, according to the laws of nature ; but the laws of nature 
obtain their effect through entelechies. But also the present state 
of the entelechy itself follows from its prior state. 

G. V. 196 (N. E. 219). As for motion, it is only a real 
phenomenon, because matter and mass, to which motion belongs, 
is not properly speaking a substance. There is, however, an image 
of action in motion, as there is an image of substance in mass ; 
and in this respect we can say that a body acts when there is 
spontaneity in its change, and suffers when it is pushed or impeded 
by another. 



VII. § 50. Antinomy of dynamical causation. 

G. II. 233. I know not whether it can be said that, when two 
equal weights simultaneously pull a body, they have no common 
effect, but each separately has half the [total] effect. For we cannot 
assign one half of the body which they pull to each weight, but 
they act as if undivided. 



THE ANALYSIS OF EXTENSION. 239 

VIII. § 51. There must he simple substances, since there are 

compounds, 

Gt. VI. 598 (D. 209; L. 406). A substaace is a being, 
capable of action. It is simple or compound. Simple substance is 
that which has no parts. Compound substance is a collection of 

simple substances or monads Compounds or bodies are pluralities; 

and simple substances, lives, souls, spirits, are unities. And every- 
where there must be simple substances, for without simple substances 
there would not be compound substances; and consequently all 
nature, is full of life. 



VIII. § 52. Extension, as distinguished from space, is 
Leibniz's starting-point. 

Or, VII. 399 (D. 265). Infinite space is not the immensity of 
God ; finite space is not the extension of bodies : as time is not their 
duration. Things keep their extension, but they do not always keep 
their space. Everything has its own extension, its own duration ; 
but it has not its own time, and does not keep its own space. 

G. IV. 394 (N. E. 700). -A.s in time we conceive nothing else 
than the disposition or series of variations which can happen in it, 
so by space we understand nothing but the possible disposition of 
bodies. And so when space is said to be extended, we take this in 
the same sense as when time is said to endure, or number to be 
numbered; for, in truth, time adds nothing to duration, nor space 
to extension, but as successive variations are in time, so in body 
those things are diverse which can be simultaneously diffused. 

G. V. 116 (N. E. 127). It must not be supposed that there 
are two extensions, the one abstract, of space, the other concrete, 
of body, the concrete being such as it is only through the abstract. 

G. VI. 585. Extension, when it is the attribute of space, is the 
continuation or diffusion of situation or locality, as the extension of 
body is the diffusion of antitypia or materiality. 

G. II. 261. You say, we must ask whether there are such 
unities in body [as mine are], and that, in order to prove these, I 
advocate entelechies. But on the contrary, I appeal to unities in 
order to prove the entelechies, although it is also true that, if the 
entelechies were otherwise proved, there would have to be true and 
real unities as well. 



240 THE ANALYSIS OF EXTENSION. 

VIII. § 53. Extension means repetition. 

P. de C. 28 (D. 176). Extension, or, if you prefer it, primary 
matter, is nothing but a certain indefinite repetition of things in so 
far as they are similar to each other or indiscernible. But just as 
number presupposes numbered things, so extension presupposes 
things which are repeated, and which have, in addition to common 
characteristics, others peculiar to themselves. These accidents, 
peculiar to each one, render actual the limits of size and shape, 
before only possible. 

G. V. 94 (N. E. 102). I believe that the idea of extension is 
posterior to that of whole and part. 

G. II. 510. That extension would remain if monads were 
removed I hold to be no more true than that numbers would remain 
if things were removed. 

G. IV. 394 (N. E. 700). Since extension is a continuous 
simultaneous repetition, ...whenever the same nature is simultane- 
ously diffused through many things, as, in gold, ductility or specific 
gravity or yellowness, in milk whiteness, in body generally resist- 
ance or impenetrability, there is said to be ejttension, although it 
must be confessed that this continuous diffusion in colour, weight, 
ductility, and other similar qualities that have a merely.specious homo- 
geneity, is only apparent, and does not occur in very small parts ; and 
thus the extension of resistance alone, which is diffused throughout 
matter, preserves this name with the rigorous investigator. But it is 
evident, from these considerations, that extension is not an absolute 
predicate, but relative to what is extended or diffused, and thus 
cannot be more separated from the nature of what is diffused than 

number from what is numbered We now ask : What other nature 

is there whose diffusion constitutes body? We have already said 
that matter is constituted by the diffusion of resistance ; but in our 
opinion there is in body something else besides matter. ...This we 
say can consist in nothing but iv ti3 Swa/iiKiS, or in the internal 
principle of change and persistence. 



VIII. § 54. Hence the essence of a substance cannot be 
extension, since a substance must be a true unity. 

G. V. 359 (N. E. 428). It is to be observed that matter, taken 
as a complete being (i.e. secondary matter, as opposed to primary, 
which is something purely passive, and consequently incomplete) is 



THE ANALYSIS OF EXTENSION. 241 

nothing but a collection (amas) or what results from it, and that 
every real collection presupposes simple substances or real unities, 
and when we consider further what belongs to the nature of these 
real unities, i.e. perception and its consequences, we are transferred, 
so to speak, into another world, that is, into the intelligible world 
of substances, whereas before we were only among the phenomena 
of the senses. 

G. II. 269, The notion of extension is relative, or extension is 
the extension of something, as we say that multitude or duration is 
the multitude or duration of something. But the nature which is 
presupposed as diffused, repeated, continued, is what constitutes the 
physical body, and can only be found in the principle of action and 
passion, since nothing else is suggested to us by phenomena. 

G. II. 135 (D. 38). Body is an aggregate of substances, and 
is not a substance properly speaking. It is consequently necessary 
that everywhere in body there should be indivisible substances, 
ingenerable and incorruptible, having something corresponding to 
souls. 

G. II. 58 (1686). If body is a substance, and not a mere 
phenomenon like the rainbow, nor a being united by accident or by 
aggregation like a heap of stones, it cannot consist of extension, 
and it is necessary to conceive in it something which we call a 
substantial form, and which corresponds in some way to a soul. 

VIII. § 55. The three kinds of point. Substances not material. 

G. IV. 478 (D. 72; L. 300). At first, when I had freed 
myself from the yoke of Aristotle, I took to the vacuum and atoms, 
„for that is the view which best satisfies the imagination. But having 
got over this, I perceived, after much meditation, that it is impos- 
sible to find the principles of a real unity in matter alone, or in that 
which is only passive, since everything in it is nothing but a collection 
or aggregate of parts ad infinitum. Now a multitude can derive its ! 
reality only from genuine units, which come from elsewhere, and are 
quite other than mathematical points, which are only extremities of ' 
the extended, and modifications of which it is certain that the con- 
tinuum cannot be composed. Accordingly, in order to find these real 
units, I was constrained to have recourse to a real and animated point, 
so to speak, or to an atom of substance which must contain some 
kind of form or active principle, so as to make it a complete being. 
It was then necessary to recall, and, as it were, to rehabilitate the 

R. L. 16 



242 THE ANALYSIS OF EXTENSION. 

substantia] form^, which are so much decried now-a-days, but in a 
way which rendered them intelligible, and separated the use to which 
they should be put from the abuse which they have suffered. I 
found, then, that the nature of substantial forms consists in force, 
and that from this follows something analogous to feeling and 
appetite ; and that thus they must be conceived after the manner of 
the notion we have of souls. 

G. III. 69. Thought, being the action of one thing on itself, 
does not occur in shapes and motions, which cannot show the 
principle of a truly internal action. 

G. II. 96. I believe that where there are only beings by 
aggregation, there will not even be real beings ; for every being by 
aggregation presupposes beings endowed with a veritable unity, 
because it derives its reality only from that of those of which it is 
composed, so that it will have none at all if each being of which it 
is composed is again a being by aggregation. ...I agree that in all 
corporeal nature there are nothing but machines (which are often 
animated), but I do not agree that there are only aggregates of 
substances, and if there are aggregates of substances, there must be 
true substances from which all these aggregates result. 

G. II. 97. What is not truly one being (un 6tre) is also not 
truly a beitig (un itre). 

G. II, 370. A point is not a certain part of matter, nor would 
an infinite number of points collected together make an extension. 

G. II. 267. -A- thing which can be divided into several (already 
actually existing) is an aggregate of several, and... is not one 
except mentally, and has no reality but what is borrowed from its 
constituents. Hence I inferred that there must be in things indivis- 
ible unities, because otherwise there will be in things no true unity, 
and no reality not borrowed. Which is absurd. For where there is 
no true unity, there is no true multiplicity. And where there is no 
reality not borrowed, there will never be any reality, since this 

must in the end belong to some subject But you [de Voider]... 

hold that the right conclusion from this is that in the mass of bodies 
no indivisible unities can be assigned. I, however, think that the 
contrary is to be concluded, namely that we must recur, in bodily 
mass, or in constituting corporeal things, to indivisible unities as 
prime constituents. Unless indeed you hold the right conclusion to 
be, that bodily masses are not themselves indivisible unities, which 
I say, but this is not the question. For bodies are always divisible, 
and even actually subdivided, but not so their constituents... . 



THE LABYRINTH OF THE CONTINUUM. 243 

G. II. 268. From the very fact that the mathematical body 
cannot be resolved into first constituents, we can certainly infer that 
it is not real, but something mental, designating nothing but the 

possibility of parts, and not anything actual And as a numbering 

number is not substance without the things numbered, so the mathe- 
matical body, or extension, is not substance without what is active 
and passive, or motion. But in real things, i.e. bodies, the parts are 
not indefinite (as in space, which is a mental thing), but are 
actually assigned in a certain way, since nature institutes actual 
divisions and subdivisions according to the varieties of motions, and 
although these divisions proceed to infinity, yet none the less every- 
thing results from certain primary constituents or real unities, but 
infinite in number. But strictly speaking, matter is not composed 
of constitutive unities, but results from them, for matter or extended 
mass is nothing but a phenomenon founded ih things, like the 
rainbow or the parhelion, and all reality belongs only to unities. 
Therefore phenomena can always be divided into lesser phenomena, 
which might appear to other subtler animals, and never attain to 
least phenomena. In fact substantial unities are not parts, but 
foundations, of phenomena. 

G. 11. 275. I do not take away body, but I recur to what it 
is, for I show that corporeal mass, which is supposed to have some- 
thing besides simple substances, is not substance, but a phenomenon 
resulting from simple substances, which alone have unity and 
absolute reality. 

IX. § 57. Difficulties about points. 

G. II. 98. The difficulties concerning the composition of the 
continuum will never be resolved, so long as extension is considered 
as making the substance of bodies. 

G. II. 77 (1686). There is no exact and precise figure in 
bodies, on account of the actual subdivision of their parts. So 
that bodies would, no doubt, be something merely imaginary and 
apparent, if there were nothing in them but matter and its modifi- 
cations. 

IX. § 58. Assertion of the actual infinite and denial of 
infinite number. 

G. I. 403. -A.11 magnitudes being infinitely divisible, there is 
none so small but that we can conceive in it an infinity of divisions, 

16—2 



244 THE LABYRINTH OF THE CONTINUUM. 

■which will never be exhausted. But I do not see what harm comes 
of this, nor what need there is to exhaust them. 

Gr, V. 144 (N. E. 161). Properly speaking, it is true that 
there are an infinity of things, i.e. that there are always more of 
them than can be assigned. But there is no infinite number, or 
line or any other infinite quantity, if these are understood as true 

wholes, as it is easy to prove The true infinite exists, strictly 

speaking, only in the Absolute, which is anterior to all compo- 
sition, and is not formed by addition of parts. 

G. V. 145 (N. E. 163). You [Locke] are mistaken in 
wishing to imagine an absolute space which is an infinite whole 
composed of parts ; there is no such thing, it is a notion which 
implies a contradiction, and these infinite wholes, with their opposed 
infinitesimals, are only in place in the calculations of geometers, 
just like imaginary roots in Algebra. 

G. VI. 629. In spite of my Infinitesimal Calculus, I admit no 
true infinite number, though I confess that the multitude of things 
surpasses every finite number, or rather every number. 

G. I. 338. Mons. Des Cartes in his reply to the second objec- 
tions, article two, agrees to the analogy between the most perfect 
Being and the greatest number, denying that this number implies a 
contradiction. It is, however, easy to prove it. Tor the greatest 
number is the same as the number of all units. But the number of 
all units is the same as the number of all numbers (for any unit 
added to the previous ones always riiakes a new number). But the 
number of all numbers implies a contradiction, which I show thus : 
To any number there is a corresponding number equal to its double. 
Therefore the number of all numbers is not greater than the 
number of even numbers, i.e. the whole is not greater than its part. 

G. V. 209 (N. E. 234). The idea of the infinite is not formed 
by extension of finite ideas. 

G. II. 305. To pass from the ideas of Geometry to the realities 
of Physics, I hold that matter is actually broken into parts less 
than any given part, or that there is no part which is not actually 
subdivided into others exercising diverse motions. 

G. II. 315. There is an actual infinite in the mode of a distri- 
butive whole, not of a collective whole. Thus something can be 
enunciated concerning all numbers, but not collectively. So it can 
be said that to every even number corresponds its odd number, and 
wee versd ; but it cannot therefore be accurately said that the multi- 
plicities of odd and even numbers are equal. 



THE LABYRINTH OF THE CONTINUUM. 245 

G. M. IV, 91. It is not necessary to make mathematical analy- 
sis depend upon metaphysical controversies, nor to make sure that 

there are in nature strictly infinitesimal lines This is why, in 

order to avoid these subtleties, I thought that, to render the 
reasoning intelligible to everybody, it sufficed in this to explain the 
infinite by the incomparable, i.e. to conceive quantities incomparably 
greater or smaller than ours. 

G. M, IV. 92. If an adversary wished to contradict our enun- 
ciation, it follows by our calculus that the error will be less than 
any error that he can assign. 

G. M. IV. 93. It is found that the rules of the finite succeed 
in the infinite. 



IX. § 59. Gontinuity in one sense denied by Leibniz. 

G. IV. 394 OS. E. 700). All repetition... is either discrete, as 
in numbered things where the parts of an aggregate are discrimi- 
nated ; or continuous, where the parts are indeterminate and can 
be assumed in infinite ways. 

G. II, 379. Space, just like time, is a certain order. ..which 
embraces not only actuals, but possibles also. Hence it is some- 
thing indefinite, like every continuum whose parts are not actual, 

but can be taken arbitrarily, like the parts of unity, or fractions 

Space is something continuous but ideal, mass is discrete, namely 
an actual multitude, or being by aggregation, but composed of an 
infinite- number of units. In actuals, single terms are prior to aggre- 
gates, in ideals the whole is prior to the part. The neglect of this 
consideration has brought forth the labyrinth of the continuum. 

G. II. 475. The mathematical continuum, like numbers, con- 
sists of mere possibility; thus infinity is necessary to it from its 
very notion. 

G. II. 278. Matter is not continuous but discrete, and actually 
infinitely divided, though no assignable part of space is without 
matter. But space, like time, is something not substantial, but 
ideal, and consists in possibilities, or in an order of coexistents that 
is in some way possible. And thus there are no divisions in it but 
such as are made by the mind, and the part is posterior to the 
whole. In real things, on the contrary, units are prior to the 
multitude, and multitudes exist only through units. (The same 
holds of changes, which are not really continuous.) 

G. II. 282. In actuals there is nothing but discrete quantity. 



246, THE LABYRINTH OP THE CONTINUUM. 

namely the multitude of monads or simple substances, which is 
greater than any number whatever in any aggregate whatever that 
is sensible or corresponds to phenomena. But continuous quantity is 
something ideal, which belongs to possibles, and to actuals considered 
as possibles. For the continuum involves indeterminate parts, while 
in actuals there is nothing indefinite — indeed in them all divisions 
which are possible are actual. ...But the science of continua, i.e. of 
possibles, contains eternal truths, which are never violated by actual 
phenomena, since the difference is always less than any assignable 
given difference. 

G. III. 583. Unity is divisible, but is not resolvable ; for the 
fractions which are parts of unity have less simple notions, because 
integers (less simple than unity) always enter into the notions of 
fractions. Several people who have philosophized, in mathematics, 
about the point and unity, have become confused, for want of 
distinguishing between resolution into notions and division into 
parts. Parts are not always simpler than the whole, though they 
are always less than the whole. 

G. IV. 491. Properly speaking, the number J in the abstract 
is a mere ratio, by no means formed by the composition of other 
fractions, though in numbered things there is found to be equality 
between two quarters and one half. And we may say as much of 
the abstract line, composition being only in concretes, or masses of 
which these abstract lines mark the relations. And it is thus also 
that mathematical points occur, which also are only modalities, i.e. 
extremities. And as everything is indefinite in the abstract line, 
we take notice in it of everything possible, as in the fractions of a 
number, without troubling ourselves concerning the divisions actually 
made, which designate these points in a different way. But in sub- 
stantial actual things, the whole is a result or assemblage of simple 
substances, or of a multiplicity of real units. And it is the confu- 
sion of the ideal and the actual which has embroiled everything and 
produced the labyrinth concerning the composition of the con- 
tinuum. Those who compose a line of points have sought first 
elements in ideal things or relations (rapports), otherwise than was 
proper; and those who have found that relations such as number, 
and space (which comprehends the order or relation of possible 
coexistent things), cannot be formed of an assemblage of points, have 
been mistaken in denying, for the most part, the first elements of 
substantial realities, as if they had no primitive units, or as if there 
were no simple substances. 



THE LABYRINTH OF THE CONTINUUM. 247 

6. V. 142 (N. E. 160). This definition, that number is a 
multiplicity of units, applies only to integers. The precise distinc- 
tion of ideas, in extension, does not depend upon magnitude : for in 
order to recognize magnitude distinctly, recourse must be had to 
integers, or to other numbers known by means of integers, so that it 
is necessary to go back from continuous to discrete quantity, in order 
to have a distinct knowledge of magnitude. 

IX. § 60. In number, space and time, the whole is prior to 

the part. 

G. I. 416 (D, 64). -A-S for indivisibles, when by these are 
meant mere extremities of a time or a line, we cannot conceive new 
extremities in them, or actual or potential parts. Thus points are 
neither large nor small, and no leap is needed to pass them. The 
continuum, however, though it has such indivisibles everywhere, is 
not composed of them. 

G. III. 591. As regards the comparison between an instant 
and unity, I add that unity is part of any number greater than 
unity, but an instant is not properly a part of time. 

G. II. 279. Extremities of a line and units of matter do not 
coincide. Three continuous points in the same straight line cannot 
be conceived. But two are conceivable : [namely] the extremity of 
one straight line and the extremity of another, out of which one 
whole is formed. As, in time, are the two instants, the last of life 
and the first of death. One unit is not touched by another, but in 
motion there is a perpetual transcreation, in this way : when a 
thing is in that condition that, by continuing its changes for an 
assignable time, there would have to be penetration in the next 
moment, each point will be in a different place, as the avoidance of 
penetration and the order of changes demand. 

G. M. VII. 18. In either order (of space or of time) [points] 
are considered nearer or more remote, according as, for the order 
of comprehension between them, more or fewer are required. 

G. II. 515. There is continuous extension whenever points are 
assumed to be so situated that there are no two between which 
there is not an intermediate point. 

G. II. 300. I agree with you [Des Bosses] that being and one 
are convertible terms ; and that unity is the beginning of numbers, 
if you are considering ratios (rationes) or priority of nature, not if 
you are considering magnitude, for we have fractions, which are 



248 THE LABYRINTH OF THE CONTINUUM. 

certainly less than unity, to infinity. The continuum is infinitely 
divisible. And this appears in the straight line, from the mere fact 
that its part is similar to the whole. Thus when the whole can be 
divided, so can the part, and similarly any part of the part. Points 
are not parts of the continuum, but extremities, and there is no 
more a smallest part of a line than a smallest fraction of unity. 

G. II. 304. Being and one are convertible terms, but as there 
is Being by aggregation, so also there is a unit by aggregation, 
although this entity and unity is semi-mental. Numbers, unities, 
fractions, have the nature of relations. And so far they can in 
some way be called beings. A fraction of unity is no less one being 
than unity itself. Nor must it be thought that formal unity is an 
aggregate of fractions, for its notion is simple, applying to divisibles 
and indivisibles, and there is no fraction of indivisibles. 

G. VII. 404 (D. 270). As for the objection [Clarke's] that 
space and time are quantities, or rather things endowed with quan- 
tity, and that situation and order are not so ; I answer, that order 
also has its quantity j there is that in it which goes before, and that 
which follows ; there is distance or interval. Relative things have 
their quantity, as well as absolute ones. For instance, ratios or 
proportions in mathematics have their quantity, and are measured 
by logarithms ; and yet they are relations. And therefore, though 
time and space consist in relations, yet they have their quantity. 



IX. § 62. Summary of the argument from the continuum to 

monads. 

G. VII. 652. In order to judge by reason whether the soul is 
material or immaterial, we must conceive what the soul and matter 
are. Everybody agrees that matter has parts, and is consequently 
a multiplicity of many substances, as would be a flock of sheep. 
But since every multiplicity presupposes true unities, it is evident 
that these unities cannot be matter, otherwise they would in turn 
be multiplicities, and by no means true and pure unities, such as 
are finally required to make a multiplicity. Thus the unities are 
properly substances apart, which are not divisible, nor consequently 
perishable. For whatever is divisible has parts, which can be 
distinguished even before their separation. However, since we are 
concerned with unities of substance, there must be force and per- 
ception in these unities themselves, for otherwise there would be no 
force or perception in all that is formed of them. 



THE THEORY OF SPACE AND TIME. 249 

IX. § 63. Since aggregates are phenomenal, there is not 
really a number of monads. 

G. II, 261. Whatever things are aggregates of many, are not 
one except for the mind, nor have any other reality than what is 
borrowed, or what belongs to the things of which they are com- 
pounded. 

G. II. 517. Aggregates themselves are nothing but pheno- 
mena, for everything except the component monads is added by 
perception alone, from the very fact of their being simultaneously 
perceived. 

G. II. 304. Instead of an infinite number, we ought to say, 

there are more than any number can express It is of the essence 

of a number, a line, or any whole, to be terminated. Hence even if 
the world were infinite in magnitude, it would not be one whole, 
nor could God be conceived, with certain of the ancients, as the soul 
of the world, not only because he is the cause of the world, but also 
because such a world would not be one body, nor could be regarded 
as an animal, nor would have, indeed, any but a verbal unity. 

X. § 66. Leibniz's arguments against the reality of space. 

G. V. 100 (N. E. 110). Things which are uniform and contain 
no variety are never anything but abstractions, like time, space, 
and the other entities of pure mathematics. 

G. VII. 363 (D. 243). These gentlemen [Newton and Clarke] 
maintain... that space is a real absolute being. But this involves 
them in great difficulties ; for such a being must needs be eternal 
and infinite. Hence some have believed it to be God himself, or 
one of his attributes, his immensity. But since space consists of 
parts, it is not a thing which can belong to God. As for my own 
opinion, I have said, more than once, that I hold space to be some- 
thing merely relative, as time is. ...For space denotes, in terms of 
possibility, an order of things which exist at the same time, con- 
sidered as existing together, without inquiring into their particular 
manner of existing. And when many things are seen together, one 

perceives that order of things among themselves If space was an 

absolute being, there would something happen, for which it would 
be impossible there should be a sufficient reason. Which is against 
my Axiom. And I prove it thus. Space is something absolutely 
uniform; and without the things placed in it, one point of space does 



250 THE THEORY OF SPACE AND TIME. 

not absolutely differ in any respect whatsoever from another point 
of space. Now from hence it follows (supposing space to be some- 
thing in itself, besides the order of bodies among themselves), that 
it is impossible there should be a reason why God, preserving the 
same situation of bodies among themselves, should have placed them 
in space after one particular manner, and not otherwise ; why every- 
thing was not placed the quite contrary way, for instance by chang- 
ing east into west. But if space is nothing else but that order or 
relation ; and is nothing at all without bodies, but the possibility of 
placing them ; then those two states, the one such as it now is, the 
other supposed to be the quite contrary way, would not at all differ 
from one another. Their difference, therefore, is only to be found 
in our chimerical supposition of the reality of space in itself. But 
in truth the one would exactly Ue the same thing as the other, they 
being absolutely indiscernible; and consequently there is no room 
to enquire after a reason of the preference of the one to the other. 

The case is the same with respect to time The same argument 

proves that instants, considered without the things, are nothing at 
all ; and that they consist only in the successive order of things. 

G. VII. 372 (D. 247). To suppose two things indiscernible, 
is to suppose the same thing under two names. And therefore to 
suppose that the universe could have had at first another position of 
time and place, than that which it actually had ; and yet that all 
the parts of the universe should have had the same situation among 
themselves, as that which they actually had ; such a supposition, I 
say, is an impossible fiction. 



X. § 67. Leibniz's theory of position. 

Gr. II. 277. The essential order of singulars, or relation to 
time and place, is to be understood of their relations to the things 
contained in time and space, both near and far, which must be 
expressed by any singular, so that in it the universe could be read, 
if the reader were infinitely perspicacious. 

G. V. 115 (N. E. 128). Time and place are only kinds of 
order. 

G. II. 347. Position is, without doubt, nothing but a mode of 
a thing, like priority or posteriority. A mathematical point itself 
is nothing but a mode, namely an extremity. And thus when two 
bodies are conceived as touching, so that two mathematical points 
are joined, they do not make a new position or whole, which would 



THE THEORY OF SPACE AND TIME. 251 

be greater than either part, since the conjunction of two extremities 
is not greater than one extremity, any more than two perfect dark- 
nesses are darker than one. 

Q. V. 140 (N. E. 157). This vacuum which can be conceived 
in time indicates, as it does in space, that time and space extend to 
possibles as well as existents. 

G, V, 142 (N. E. 159). If there were a vacuum in space (e.g. 
if a sphere were empty inside) its magnitude could be determined ; 
but if there were a vacuum in time, i.e, a duration without changes, 
it would be impossible to determine its length. Hence it follows 
that we can refute a man who says that two bodies, between which 
there is a vacuum, touch... but we cannot refute a man who says 
that two worlds, of which one is after the other, touch as regards 
duration, so tha,t one necessarily begins when the other stops. . . . 
If space were only a line, and if body were immovable, it would not 
be possible either to determine the length of the vacuum between 
two bodies. 

Qt, VII. 400 (D. 265). I will here show how men come to 
form to themselves the notion of space. They consider that many 
things exist at once, and they observe in them a certain order of 
coexistence, according to which the relation of one thing to another 
is more or less simple. This order is their situation or distance. 
When it happens that one of those coexistent things changes its 
relation to a multitude of others, which do not change their rela- 
tions among themselves ; and that another thing, newly come, 
acquires the same relation to the others, as the former had; we 
then say it is come into the place of the former ; and this change 
we call a motion in that body, wherein is the immediate cause of 
the change. And though many, or even all the coexistent things 
should change according to certain known rules of direction and 
swiftness ; yet one may always determine the relation of situation, 
which every coexistent acquires with respect to every other co- 
existent ; and even that relation which any other coexistent would 
have to this, or which this would have to any other, if it had not 
changed, or if it had changed any otherwise. And supposing or 
feigning that among those coexistents there is a sufficient number 
of them which have undergone no change ; then we may say that 
those that have such a relation to those fixed coexistents, as others 
had to them before, have now the same place which those others 
had. And that which comprehends all those places, is called space. 
Which shows that, in order to have an idea of place, and conse- 



252 THE THEORY OF SPACE AND TIME. 

quently of space, it is sufficient to consider these relations, and the 
rules of their changes, without needing to fancy any absolute 
reality out of the things whose situation we consider ; and, to give 
a kind of definition : place is that, which we say is the same to A 
and to B, when the relation of the coexistence of B with C, E, F, G, 
e<c.,- agrees perfectly with the relation of the coexistence, which A 
had with the same C, E, F, G, etc., supposing there has been no 
cause of change in C, E, F, G, etc. It might be said also, without 
entering into any farther particularity, that place is that, which is 
the same in different moments to different existent things, when 
their relations of coexistence with certain other existents, which are 
supposed to continue fixed from one of those moments to the other, 
agree entirely together. And fixed existents are those, in which 
there has been no cause of any change of the order of their coexist- 
ence with others ; or (which is the same thing) in which there has 
been no motion. Lastly spcbce is that which results from places 
taken together. And here " it may not be amiss to consider the 
difference between place, and the relation of situation, which is in 
the body that fills up the place. For the plcice of A and B is the 
same ; whereas the relation of A to fixed bodies is not precisely and 
individually the same as the relation which B (that comes into its 
place) will have to the same fixed bodies ; but these relations agree 
only. For two different subjects, as A and B, cannot have precisely 
the same individual affection; it being impossible that the same 
individual accident should be in two subjects, or pass from one 
subject to another. But the mind, not contented with an agree- 
ment, looks for an identity, for something that should be truly the 
same ; and conceives it as being extrinsic to these subjects : and this 
is what we here call place and space. But this can only be an ideal 
thing; containing a certain order, wherein the mind conceives the 
application of relations. 

G. II. 271. Unless I am mistaken, the order of singulars is 
essential to particular parts of space and time, and from these [the 
singulars] universals are abstracted by the mind. 

X. § 68. The relation of monads to space a fundamental 
difficulty of monadism. 

G. II. 305, There is no part of matter which does not contain 
monads. 

G. II. 112 (1687). Our body must be affected in some way by 



THE THEORY OF SPACE AND TIME. 253 

the changes in all others. Now to all motions of our body corre- 
spond certain more or less confused perceptions or thoughts of our 
soul ; hence the soul also will have some thought of all the motions 
of the universe. 

G. II. 438. Between the appearance of bodies to us and their 
appearance to God, there is the same kind of difference as between 
a scenograph and an ichnograph. For scenographs are different 
according to the situation of the spectator, while the ichnograph, or 
geometrical representation, is unique. 

G. VI. 608 (D. 218; L. 220). If simple substances did not 
differ in their qualities, there would be no means of perceiving any 

change in things Assuming the plenum, each place would only 

receive, in any motion, the equivalent of what it had had, and one 
state of things would be indiscernible from another. 

G. V. 24 (N, E. 25). The least impression reaches every body, 
and consequently reaches the one whose motions correspond to the 
actions of the soul. 



X. § 69. Leibniz's early views on this subject. 

G. I. 52 (1671). My proofs [of immortality, and of the nature 
of God and the mind] are based on the difficult doctrine of the 
point, the instant, indivisibles, and conation ; for just as the actions 
of body consist of motion, so the actions of mind consist of 
conation, or, so to speak, the minimum or point of motion ; while 
mind itself consists properly in only a point of space, whereas a 
body occupies a place. Which I clearly prove — to speak of it only 
popularly — by the fact that the mind must be in the place of 
concourse of all the motions which are impressed on us by the 
objects of sense ; for if I am to conclude that a body presented to 
me is gold, I perceive together its lustre, clink, and weight, and 
thence conclude that it is gold; so that the mind must be in a 
position where all these lines of sight, hearing, and touch meet, and 
consequently in a point. If we give the mind a greater place than 
a point, it is already a body, and has parts external to each other ; 
it is therefore not intimately present to itself, and accordingly 
cannot reflect on all its parts and actions.... But assuming that the 

mind does consist in a point, it is indivisible and indestructible 

I almost think that every body (Leib), whether of men or animals, 
vegetables or minerals, has a kernel of its substance, which is 
distinguished from the caput niortuum. . . . 



254 THE THEORY OF SPACE AND TIME. 

G. I, 64. If now this kernel of substance, consisting in a 
physical point (the proximate instrument, and as it were the 
vehicle, of the soul, which is constituted in a mathematical point), 
always remains, it matters little whether all gross matter... is left 
over. 



X. § 70. His middle views. 

G. IV. 482 (D. 76 ; L. 311) (1695). Only atoms of substance, 
i.e. real units absolutely devoid of parts, are the sources of actions, 
and the absolute first principles of the composition of things, and, 
as it were, the ultimate elements in the analysis of substantial 
things. They might be called meta/physical points ; they have some- 
thing of the nature of life and they have a kind of perception, and 
mathematical points are their points of view for expressing the 
universe. But when corporeal substances are contracted, all their 
organs together make but one physical point for us. Thus physical 
points are only apparently indivisible. Mathematical points are 
exact, but they are only modalities. None but metaphysical or 
substantial points (consisting of forms or souls) are exact and real. 

G. IV. 484 (D. 78; L. 314) (1695). The organised mass, in 
which is the point of view of the soul, is more nearly expressed by 
the soul. 

G. IV. 512 (D. 122) (1698). Nothing hinders souls, or at 
least things analogous to souls, from being everywhere, although the 
dominant, and hence intelligent, souls, like those of men, cannot be 
everywhere. 



X. § 71. His later views. 

G. IV. 574 ("«• 1700). It seems that it is more exact to say 
that spirits are where they operate immediately than to say... that 
they are nowhere. 

G. II. 450 (1712). The explanation of all phenomena by 
nothing but the mutually conspiring perceptions of monads, setting 
aside corporeal substance, I hold to be useful for the fundamental 
inspection of things. And in this manner of exposition, space 
becomes the order of coexistent phenomena, as time of those that 
are successive ; and there is no spatial or absolute distance or pro- 
pinquity of monads : to say that they are massed together in a 



THE THEORY OF SPACE AND TIME. 255 

point, or disseminated in space, is to make use of certain fictions of 
our soul, since we take pleasure in imagining things which can only 
be conceived. In this way of looking at things, there is no exten- 
sion or composition of the continuum, and all difficulties about 
points vanish. 

G. V. 205 (N. E. 230) (1704). The schools have three kinds 
of ubiety, or ways of existing somewhere. The first is called circum- 
scriptive, which we attribute to bodies that are in space, which are 
in it punctatim, so that they are measured according as points can 
be assigned to the situated thing corresponding to the points of 
space. The second is definitive, where we can define, i.e. determine, 
that the situated thing is in a certain space, without being able to 
assign precise points or proper places exclusively to what is there. 
It is thus people judge that the soul is in the body, not believing it 
possible to assign an exact point, where is the soul, or something of 
the soul, without its being also in some other point. . . .The third 
sort of ubiety is repletive, which is attributed to God, who fills the 
whole universe even more eminently than spirits are in bodies, for 
he operates immediately on all creatures by continually producing 
them, whereas finite spirits cannot exercise any immediate influence 
or operation. I know not whether this doctrine of the schools 
deserves to be turned into ridicule, as it seems people endeavour to 
do. However we can always attribute a kind of motion to souls, at 
least in relation to the bodies with which they are united, or in 
relation to their manner of perception. 

G. VI. 598 (D. 209; L. 408) (1714). There are simple 
substances everywhere, separated from each other, in fact {ef- 
fectivement), by their own actions, which continually change their 
relations. 

G. III. 623 (1714). We must not conceive extension as a 
real continuous space, strewn with points. These are fictions proper 
to content the imagination, but in which reason does not find what 
it requires. Nor must we conceive that Monads, like points in a 
real space, move, push, or touch each other; it is enough that 
phenomena make it seem so, and this appearance partakes of truth 
in so far as these phenomena are founded, i.e. agree with each 
other. 

G. II. 339 (1707). A simple substance, though it has no 
extension in itself, yet has position, which is the foundation of 
extension, since extension is the simultaneous continuous repetition 
of position. 



256 THE THEORY OF SPACE AND TIME. 

G. II. 370 (1709). I do not think it fitting to consider souls 
as in points. Some one might perhaps say that they are only in a 
place by operation... or rather,... that they are in a place by corre- 
spondence, and are thus in the whole organic body which they 
animate. Meanwhile I do not deny a certain real metaphysical 
union between the soul and the organic body... according to which 
it could be said that the soul really is in the body. 

G. II. 378 (1709). Although the places of monads are desig- 
nated by modifications or terminations of parts of space, yet the 
monads themselves are not modifications of a continuous thing. 
Mass and its diffusion result from monads, but not space. For space 
...is a certain order, embracing not only actuals but also possibles. 

G. II. 436 (1712). We ought not to say of monads, any more 
than of points and souls, that they are parts of bodies, that they 
touch each other, or that they compose bodies. 

G-, II, 438 (1712). God sees not only single monads and the 
modifications of each monad, but also their relations, and in this 
consists the reality of relations and truths. 

G, II. 444 (1712). Monads per se have not even any relative 
situation — i.e. no real one — which extends beyond the order of 
phenomena. 

G. II. 253 (1703). Monads, though they are not extended, 
yet have something of the nature of position in extension, i.e. they 
have a certain ordered relation of coexistence to other things, 
through the machine which they dominate (cui praesunt). And I 
do not think that any finite substances exist separated from every 
body, nor consequently are without position or order in regard to 
the other things which coexist in the universe. Extended things 
involve in themselves many things having position, but things 
which are simple, though they have no extension, yet must have 
position in extension, although it is impossible to designate this 
punctatim as in incomplete phenomena. 

G. II. 277 (1704—5). My unities or simple substances are not 
diffused, ...nor do they constitute a homogeneous whole, for the 
homogeneity of matter is obtained only by a mental abstraction, 
when we consider only things that are passive and therefore incom- 
plete. 

X. § 72. Time and change. 

G. VII. 373 (D. 249). It is a similar, i.e. impossible, fiction, 
to imagine that God might have created the world some millions of 



THE THEORY OF SPACE AND TIME. 257 

years sooner. Those who agree to fictions of this sort will be 
unable to reply to those who would argue for the eternity of the 
world. For since God does nothing without a reason, and since no 
reason is assignable why he should not have created the world 
sooner, it will follow, either that he created nothing at all, or that 
he produced the world before every assignable time, i.e. that the 
world is eternal. But when it is shown that the beginning, what- 
ever it is {quel qu'il soit), is always the same thing, the question 
why it was not otherwise ceases. 

G. VII. 402 (D. 268). It cannot be said that a certain dura- 
tion is eternal ; but that things which continue always are eternal, 
by always gaining new extension. Whatever exists of time and of 
duration, being successive, perishes continually; and how can a 
tiling exist eternally which (to speak exactly) does never exist at 
all ? For how can a thing exist, whereof no part does ever exist ? 
Nothing of time does ever exist, but instants ; and an instant is not 
even itself a part of time. 

G. VII. 408 (D. 274). From extension to duration, non valet 
consequentia. Though the extension of matter were unlimited, yet 
it would not follow that its duration would be also unlimited ; nay 
even, a parte ante, it would not follow that it had no beginning. 
If it is of the nature of things in the whole to grow uniformly in 
perfection, the universe of creatures must have had a beginning. . . . 
Besides, the world's having a beginning does not derogate from the 
infinity of its duration a parte post; but bounds of the universe 
would derogate from the infinity of its extension. 

G. III. 581. As for succession, where you [Bourguet] seem to 
judge, Sir, that one must conceive a first fundamental instant, as 
unity is the foundation of numbers, and as the point is also the foun- 
dation of extension : to this I might answer that the instant is also 
the foundation of time, but as there is no point in nature which is 
fundamental with regard to all other points, and so to speak the 
seat of God, so I do not see that it is necessary to conceive a 
principal instant. I admit, however, that there is this difference 
between instants and points, that one point of the universe has not 
the advantage of priority of nature over another, whereas the 
preceding instant has, over the Succeeding instant, the advantage of 
priority not of time only, but also of nature. But it is not neces- 
sary on that account that there should be a first instant. There is 
a difference, in this, between the analysis of necessary things and 
that of contingent things Thus the analogy from numbers to 

B. L. 17 



258 THE THEORY OF SPACE AND TIME. 

instants does not hold here. It is true that the notion of numbers 
is resolvable at last into the' notion of unity, which is no longer 
resolvable, and may be considered as the primitive number. But it 
does not follow that the notions of the various instants are resolv- 
able at last into a primitive instant. However, I do not venture to 
deny that there was a first instant. Two hypotheses may be formed, 
either that nature is always equally perfect, or that it always grows 
in perfection. ...[In the first case] it is more likely that there is no 
beginning. [In the second case] . . .the matter could still be explained 
in two ways, namely by the ordinates of a hyperbola or by those of 
a triangle. According to the hypothesis of the hyperbola, there 
would be no beginning... but according to the hypothesis of the 

triangle, there would have been a beginning I see no way of 

showing demonstratively by pure reason which should be chosen. 

G. VII. 415 (D. 281). The author [Clarke] objects here, that 
time cannot be an order of successive things, because the quantity 
of time may become greater or less, and yet the order of successions 
continue the same. I answer, this is not so. For if the time be 
greater, there will be more successive and like states interposed ; 
and if it be less, there will be fewer ; seeing there is no vacuum, 
nor condensation, nor penetration (if I may so speak) in times, any 
more than in places. 

G. II. 183. Time is neither more nor less a being of reason 
than space. To coexist and to pre- or post-exist, are something 
real ; they would not be so, I admit, according to the ordinary view 
of matter and substance. 

G. V. 139 (N. E. 156). Time is the measure of motion, i.e. 
uniform motion is the measure of non-uniform motion. 



X. § 74 Leibniz held confusedly to an objective counterpart 
of space and time. 

G. VII. 329. Every primitive entelechy must have perception. 
For every first entelechy has internal variation, according to which 
its external actions also vary. But perception is nothing but that 
very representation of external by internal variation. Since, there- 
fore, primitive entelechies are dispersed everywhere throughout 
matter — which can easily be shown from the fact that principles of 
motion are dispersed throughout matter — the consequence is, that 
souls also are dispersed everywhere throughout matter. 



THE NATURE OF MONADS IN GENERAL. 259 

Q-, VI. 405, As soon as we admit that God exists, we must 
admit that he exists necessarily. Now this privilege does not 
belong to the three things of which we have been speaking [motion, 
matter and space]. 

Cr, VII. 375 (D. 251). God perceives things in himself. 
Space is the place of things, and not the place of God's ideas. 



XI. § 75. Perception. 

G. VI. 599 (D. 209 ; L. 409). Perceptions in the Monad are 
produced one from another according to the laws of appetites or of 
the final causes of good and evil, which consist in observable per- 
ceptions, regular or irregular. 

G. I. 383 (1686). it is not necessary that what we conceive 
of things outside us should be perfectly similar to them, but that it 
should express them, as an ellipse expresses a circle seen obliquely, 
so that to each point of the circle a point of the ellipse corresponds, 
and vice versd, according to a certain law of relation. For... each 
individual substance expresses the universe in its own way, much as 
the same town is diversely expressed according to different points of 
view. 

G. V. 101 (N. E. III). A state without thought in the soul, 
and an absolute rest in body, seem to me equally contrary to nature, 
and without example in the world. A substance which is once in 
action will be so always, for all impressions remain, and are only 
mixed with other new ones. 

G. VI. 576 (D. 187). When Mr Locke declares that he does 
not understand how the variety of ideas is compatible with the 
simplicity of God, it seems to me that he ought not hence to derive 
an objection to Father Malebranche ; for there is no system which 
can make such a thing intelligible. 

G. VI. 577 (D. 188). Mr Locke asks whether an indivisible 
and unextended substance can have at the same time modifications 
which are difierent and even refer to inconsistent objects. I answer 
that it can. What is inconsistent in the same object is not incon- 
sistent in the representation of difierent objects, which are conceived 
at the same time. For this it is not necessary that there should be 
different parts in the soul, as it is not necessary that there should be 
difierent parts in the point, though different angles meet in it. 

G. VI. 608 (D. 219; L. 222). I assume as admitted that 
every created being, and consequently the created Monad, is subject 

17—2 



260 THE NATURE OF MONADS IN GENERAL. 

to change, and further that this change is continual in each. It 
follows from what has just been said, that the natural changes of 
the Monads come from an internal principle, since an external 
cause can have no influence upon their inner being. But besides 
the principle of the change, there must be a particular series of 
changes [mm cUtail de ce qui change], which constitutes, so to speak, 
the specific nature and variety of the simple substances. This 
particular series of changes must involve a multiplicity in the 
unit, or in that which is simple. For, as every natural change 
takes place gradually, something changes and something remains 
unchanged; and consequently a simple substance must be affected 
and related in many ways, although it has no parts. 

G. VI. 609 (D. 220; L. 226). We have in ourselves expe- 
rience of a multiplicity in a simple substance, when we find that 
the least thought of which we are conscious involves variety in its 
object. Thus all those who admit that the soul is a simple sub- 
stance should admit this multiplicity in the Monad. 

G. VI. 327. It is true that the same thing can be represented 
differently ; but there must always be an exact relation between the 
representation and the thing, and consequently between different 
representations of the same thing. 

G. VII. 410 (D. 275). The author [Clarke] speaks as if he 
did not understand how, according to my opinion, the soul is a 
representative principle. Which is, as if he had never heard of my 
pre-established harmony. I do not assent to the vulgar notions, 
that the images of things are conveyed by the organs of sense to the 
soul. For, it is not conceivable by what passage, or by what means 
of conveyance, these images can be carried from the organ to the 
soul. This vulgar notion in philosophy is not intelligible, as the 
new Cartesians have sufficiently shown. It cannot be explained, 
how immaterial substance is affected by matter : and to maintain 
an intelligible notion thereupon, is having recourse to the scholastic 
chimerical notion of I know not what inexplicable species inten- 
tionales, passing from the organs to the soul. Those Cartesians saw 

the difficulty, but they could not explain it But I think I have 

given the true solution of that enigma. 

G. II. 71 (1686). It is the nature of the soul to express what 
is happening in bodies, being so created originally that the series of 
its thoughts agrees with the series of motions. 

G. II. 74 (1686). The nature of every substance involves a 
general expression of the whole universe, and the nature of the soul 



THE NATURE OF MONADS IN GENERAL. 261 

involves more particularly a more distinct expression of what is now 
happening in relation to its body. 

G. III. 575. Perception is, for me, the representation of a 
multiplicity in what is simple ; and appetite is the tendency from 
one perception to another : now these two things are in all Monads, 
for otherwise a monad would have no relation to other things. I 
do not know, Sir, how you [Bourguet] can derive any Spindzism 
from this ; that is jumping to conclusions rather too fast. On the 
contrary, it is just by means of these monads that Spinozism is 
destroyed, for there are as many true substances, and, so to speak, 
living mirrors of the universe always subsisting, or concentrated 
universes, as there are Monads, whereas according to Spinoza there 
is only a single substance. He would be right, if there were no 
monads ; then everything except God would be passing, and would 
sink into mere accidents and modifications, since there would not be 
in things the basis of substances, which consists in the existence of 
monads. 

F. de C. 62 (D. 182). [Spinoza] is wrong in thinking that 
affirmation or negation is volition, since volition involves also the 
reason of the good. 

G. II. 317. -A. universal is one in many, or the similarity of 
many ; but when we perceive, many are expressed in one, namely 
the percipient. You see how far apart these are. 

G. II. 256, I recognize monads that are active fer se, and 
in them nothing can be conceived except perception, which in turn 
involves action. 



XI. § 77. Perception not due to action of the perceived on 
the percipient. 

G. IV. 495 (D. 86). I take care not to admit that the soul 
does not know bodies, though this knowledge arises without influ- 
ence of the one on the other. 

G. IV. 484 (D. 77; L. 313). God at first so created the soul, 
or any other real unity, that everything must arise in it from its 
own inner nature, with a perfect spontaneity as regards itself, and 
yet with a perfect conformity to things outside of it And accord- 
ingly, since each of these substances accurately represents the whole 
universe in its own way and from a certain point of view, and the 
perceptions or expressions of external things come into the soul at 
their appropriate time, in virtue of its own laws, as in a world by 



262 THE NATURE OF MONADS IN GENERAL. 

itself, and as if there existed nothing but God and the soul, ...there 
will be a perfect agreement between all these substances, which will 
have the same result as if they had communication with one another 
by a transmission of species or qualities, such as the mass of ordinary 
philosophers suppose. 

G. VI. 607 (D. 218; L. 219). There is no way of explaining 
how a Monad can be altered in quality or internally changed by 
any other created thing ; since it is impossible to change the place 
of anything in it or to conceive in it any internal motion which 
could be produced, directed, increased or diminished therein, although 
all this is possible in the case of compounds, in which there are 
changes among the parts. The monads have no windows, through 
which anything could come in or go out. Accidents cannot separate 
themselves from substances nor go outside of them, as the " sensible 
species " of the scholastics used to do. Thus neither substance nor 
accident can come into a monad from outside. 

G. II. 12 (1686). Every singular substance expresses the 
whole universe in its own way, and in its notion are comprised all 
its events with all their circumstances, and the whole series of 
external things. 

G. II. 136 (D. 38). Each of these substances contains in it's 
nature legem continuationis seriei suarum, operationum, and all that 
has happened and will happen to it. All its actions come from its 
own nature, except for its dependence upon God. 

G. II. 603. I do not believe that a system is possible, in which 
Monads act on each other, because there seems to be no possible 
way of explaining such action. I add that an influence is also 
superfluous, for why should a monad give to another monad what it 
already has? For this is the very nature of substance, that its 
present should be big with the future, and that all things can be 
understood by means of one, unless indeed God should miraculously 
interfere. 

G. IV, 440 (1686). Nothing can happen to us but thoughts 
and perceptions, and all our future thoughts and perceptions are 
only consequences, though contingent ones, of our previous thoughts 
and perceptions, so much so that if I were capable of considering 
distinctly all that happens or appears to me at the present time, I 
could see in it all that will happen or appear to me for ever ; which 
would not fail, and would happen to me just the same, if all that is 
outside of me were destroyed, provided only that God and I re- 
mained. 



THE NATURE OF MONADS IN GENERAL. 263 

G. II. 119. Only indivisible substances and their different 
states are absolutely real. 



XI. § 79. The pre-established harmony. 

G. II. 58 (1686). Only the hypothesis of the concomitance or 
agreement of substances inter se explains everything in a manner 
which is conceivable and worthy of God ; it is even demonstrative 
and inevitable, in my opinion, according to the proposition which 
we have just established [that in every proposition the notion of the 
predicate is contained in that of the subject]. 

G. I. 382 (1686). I believe that every individual substance 
expresses the whole universe in its own way, and that its following 
state is a consequence (though often a free one) of its preceding 
state, as if there were nothing but God and it in the world j but as 
all substances are a continual production of the sovereign Being, 
and express the same universe or the same phenomena, they agree 
exactly with each other. 

G. VII. 311. Every substance has something of the infinite, 
in so far as it involves its cause, i.e. God, that is, it has some trace 
of omniscience and omnipotence ; for in the perfect notion of each 
individual substance there are contained all its predicates, alike 
necessary and contingent, past, present, and future ; nay each sub- 
stance expresses the whole universe according to its situation and 
aspect, in so far as other things are referred to it ; and hence it is 
necessary that some of our perceptions, even if they be clear, should 
be confused, since they involve things which are infinite, as do 
our perceptions of colour, heat, etc. 

G. II. 68 (1686). The hypothesis of concomitance is a conse- 
quence of the notion which I have of substance. For according to 
me the individual notion of a substance involves all that will ever 
happen to it. 

G. II. 136 (D. 38). Each substance expresses the whole 
universe, but some more distinctly than others, especially each in 
regard to certain things, and according to its point of view. The 
union of soul and body, and even the operation of one substance on 
another, consists only in this perfect mutual agreement, purposely 
established by the order of the first creation, in virtue of which 
each substance, following its own laws, falls in with what the others 
demand, and the operations of the one thus follow or accompany 
the operation or change of the other. 



264 SOUL AND BODY. 

G. II. 226. Certainly, in my opinion, there is nothing in the 
universe of creatures which does not need, for its perfect concept, 
the concept of every other thing in the universe of things, since 
everything influences everything else, so that if it were taken away 
or supposed different, all the things in the world would have been 
different from those that now are. 

G. III. 143. It is true there is miracle in my system of pre- 
established Harmony, and that God enters into it extraordinarily, 
but it is only in the beginning of things, after which everything 
goes its own way in the phenomena of nature, according to the laws 
of souls and bodies. 

G. III. 144. It seems to me that I may say that my hypo- 
thesis (concerning the pre-established Harmony) is not gratuitous, 
since I believe I have made it appear that there are only three 
possible hypotheses [the influxus physicus, occasionalism, and the 
pre-established harmony], and that only mine is at once intelligible 
and natural ; but it can even be proved d, priori. 



XII. § 83. The three classes of monads. 

G. VI. 600 (D. 211 ; L. 411). It is well to make a distinction 
between perception, which is the internal state of the Monad repre- 
senting external things, and apperception, which is the consciousness 
or the reflective knowledge of this internal state, and which is not 
given to all souls, nor to the same soul at all times. It is for lack 
of this distinction that the Cartesians have made the mistake of 

ignoring perceptions of which we are not conscious Genuine 

reasoning depends upon necessary or eternal truths, such as those 
of logic, of number, of geometry, which produce an indubitable 
connection of ideas and infallible inferences. The animals in which 
these inferences do not appear are called the brutes; but those 
which know these necessary truths are properly those which are 
called rationed animals, and their souls are called spirits \esprits\ 
These souls have the power to perform acts of reflection, and to 
consider what is called the ego, substance, soul, spirit, in a word, 
immaterial things and truths. 

G. VI. 604 (D. 215; L. 420). As regards the rational soul 
or spirit, there is in it something more than in the monads or 
even in mere souls. It is not only a mirror of the universe of 

created beings, but also an image of the Deity It is for this 

reason that all spirits, whether of men or genii, entering in virtue 



SOUL AND BODY. 265 

of reason and of eternal truths into a kind of fellowship with God, 
are members of the City of God, i.e. of the most perfect state, 
formed and governed by the greatest and best of Monarchs. 

G. VI. 610 (D. 220; L. 230). If we are to give the name 
of Soul to everything which has perceptions and appetites in the 
general sense which I have just explained, then all simple substances 
or created Monads might be called souls ; but as feeling is some- 
thing more than a bare perception, I think it right that the 
general name of Monads or Entelechies should suffice for simple 
substances which have perception only, and that the name of Souls 
should be given only to those in which perception is more distinct 
and accompanied by memory. 

G. IV. 479 (D. 73 ; L. 303). We must not confound or in- 
differently mix, with other forms or souls. Spirits or the reasonable 
soul, which are of a higher order, and have incomparably more 
perfection than these forms buried in matter — which in my opinion 
are to be found everywhere — being like little gods in comparison 
with these, being made in the image of God, and having in them 
some ray of the Divine light. For this reason, God governs 
spirits as a prince governs his subjects, and indeed as a father 
cares for his children ; while, on the other hand, he deals with 
other substances as an engineer works with his machines. Thus 
spirits have special laws, which put them above the revolutions 
.of matter through the very order which God has placed there ; 
and it may be said that everything else is made only for them, 
these revolutions themselves being arranged for the felicity of the 
good and the punishment of the wicked. 

G. V. 218 (N. E. 246). The consciousness or feeling of the 
£go proves a moral or personal identity. And it is by this that I 
distinguish the incessahility of a brute's soul from the immortality of 
the soul of man : both preserve physical and real identity, but as for 
man, it is conformable to the rules of the Divine Providence that 
the soul should retain also a moral identity apparent to ourselves, so 
as to constitute the same person, capable consequently of feeling 
chastisements and rewards. 

G. V. 219 (N. E. 247). As for the Self, it will be well to 
distinguish it from the appearance of Self and from conscious- 
ness. The Self constitutes real and physical identitj', and the 
appearance of Self, accompanied by truth, joins personal identity 
to it. 

G. III. 622. [-A.11 monads] have perception... a,nd appetite..., 



266 SOUL AND BODY. 

which is called passion in animals, and tvill where perception is an 
understanding. 

G. v. 284 (N. E. 331). It is essential to substances to act, 
to created substances to suflfer, to spirits to think, to bodies to 
have extension and motion. That is, there are sorts or species to 
which an individual cannot (naturally at least) cease to belong, 
when it has once belonged to them. 

G. V. 290 (N. E. 338). [In man] reason is a fixed attribute, 
belonging to each individual, and never lost, though we cannot 
always perceive it. 

G. VII. 529 (D. 190). You next ask my definition of sotd. I 
reply, that soul may be employed in a broad and in a strict sense. 
Broadly speaking, sotd will be the same as life or vital principle, 
i.e. the principle of internal action existing in the simple thing or 
monad, to which external action corresponds. And this correspond- 
ence of internal and external, or representation of the external in 
the internal, of the composite in the simple, of multiplicity in unity, 
really constitutes perception. But in this sense soul is attributed 
not only to animals, but also to all other percipient beings. In the 
strict sense, soul is employed as a nobler species of life, or sentient 
life, where there is not only the faculty of perceiving, but in addition 
that of feeling, inasmuch, indeed, as attention and memory are added 
to perception. Just as, in turn, mind is a nobler species of soul, i.e. 
mind is rational soul, where reason, or ratiocination from universality 
of truths, is added to feeling. As, therefore, mind is rational soul, 
so soul is sentient life, and life is perceptive principle. 



XII. § 84. Activity and passivity. 

G. IV. 486 (D. 79 ; L. 317). The customary ways of speaking 
can still be quite well preserved [in my system]. For we may say 
that the substance whose disposition explains a change in an in- 
telligible way (so that we may hold that it is this substance to 
which the others have on this point been adapted from the beginning, 
according to the order of the decrees of God) is the substance which, 
in respect of this change, we should conceive as acting upon the 
others. 

G. VI. 615 (D. 225; L. 245). A creature is said to act 
outwardly in so far as it has perfection, and to suffer- in relation to 
another in so far as it is imperfect. Thus action is attributed to a 
Monad in so far as it has distinct perceptions, and passion in so far 



SOUL AND BODY. 267 

as its perceptions are confused. And one created thing is more 
perfect than another in this, that there is found in the more perfect 
that which serves to explain a priori what takes place in the other, 
and it is on this account that the former is said to act upon the 
latter. But in simple substances the influence of one Monad upon 
another is only ideal, and it can have its effect only through the me- 
diation of God, in so far as in the ideas of God one Monad rightly 
claims that God, in regulating the others from the beginning of things, 
should have regard to it. ...And it is thus that, among creatures, 
activities and passivities are mutual. For God, comparing two 
simple substances, finds in each reasons which oblige him to adapt 
the other to it, and consequently what is active in certain respects 
is passive from another point of view ; active in so far as what we 
distinctly know in it serves to give a reason for what takes 
place in another, and passive in so far as the reason for what takes 
place in it is to be found in that which is distinctly known in 
another, 

G, IV. 441 (1686). When a change occurs by which several 
substances are affected (as in fact every change affects them all), I 
believe we may say that the one which thereby immediately passes 
to a greater degree of perfection or to a more perfect expression, 
exerts its power, and acts, and that which passes to a less degree 
makes known its feebleness, and suffers. Also I hold that every 
action of a substance which has perception implies some joy, and 
every passion some pain. 

G. II. 13 (1686). The action of one finite substance on another 
consists only in the increase in the degree of its expression joined to 
the diminution of that of the other, inasmuch as God has formed 
them beforehand so that they should agree together. 

G. V. 201 (N. E. 324). I do not know whether one can say 
that the same being is called action in the agent and passion in the 
patient, and is thus in two subjects at once, like a relation, or 
whether it is not better to say that they are two beings, one in the 
agent, the other in the patient. 



XII. §, 86. Materia prima as an element in each monad. 

G. VII. 322 (N. E. 720). Substances have metaphysical 
matter or passive power in so far as they express anything con- 
fusedly, active power in so far as they express anything distinctly. 



268 SOUL AND BODY. 

G. III. 636. As Monads (except the primitive one) are subject 
to passions, they are not pure forces; they are the foundation, 
not only of actions, but also of resistances or passivities, and their 
passions are in confused perceptions. It is this which involves 
matter or the infinite in number. 

G. II. 516. -A. substance acts as much as it can, unless it is 
impeded; even a simple substance, however, is impeded, but not 
naturally unless internally by itself. And when a monad is said to 
be impeded by another, this is to be understood of the representa- 
tion of the other in itself. 

G. II. 306. Materia prima... ]j&\ the primitive passive power, 
or principle of resistance, which does not consist of extension, 
but of what extension needs, and complements the entelechy or 
primitive active power, so as to produce the complete substance or 

Monad We hold that such matter, i.e. the principle of passion, 

persists, and adheres to its own Entelechy. 

G. II. 325. Although God could, by his absolute power, 
deprive a created substance of nvateria secunda, yet he cannot 
deprive it of materia prima ; for he would thus make it Actus purus, 
such as he alone is. 

G. II. 368. [The materia primu of one Monad] does not 
increase mass, or the phenomenon resulting from Monads, any more 
than a point increases a line. 



XII. § 87. Materia prima the source of finitude, plurality 
and matter, 

G. VI. 546 (D. 169). God alone is above all matter, since he 
is its Author ; but creatures free or freed from matter would be at 
the same time detached from the universal connection, and like 
deserters from the general order. 

G. II. 324. To remove these [Intelligences] from bodies and 
place, is to remove them from the universal connection and order of 
the world, which is made by relations to time and place. 

G. II. 412. Whoever admits the pre-established Harmony, 
cannot but admit also the doctrine of the actual division of matter 
into infinite parts. 

G. II. 460. You [Des Bosses] ask further, why there should 
be actually infinitely numerous monads? I answer, for this their 
possibility will suffice, since it is better that the works of God should 
be as splendid as possible ; but the same is required by the order of 



SOUL AND BODY. 269 

things, otherwise phenomena will not correspond to all assignable 
percipients. And indeed in our perceptions, however distinct, we 
conceive that confused ones are contained to any degree of small- 
ness ; and thus monads will correspond to these, as to greater and 
more distinct ones. 

G. II. 248. You [de Voider] desire a necessary connection 
between matter (or resistance) and active force, so as not to join 
them arbitrarily. But the cause of the connection is, that every 
substance is active, and every finite substance is passive, while 
resistance is connected with passion. Therefore such a conjunction 
is demanded by the nature of things. 

XII. § 90. First theory of Soul and Body. 

G. VI. 539 (D. 163). When I am asked if these [principles of 
life] are substantial forms, I reply by a distinction : for if this term 
is taken, as M. Des Cartes takes it, when he maintains... that the 
reasonable soul is the substantial form of man, I should answer yes. 
But I should say «o, if any one understood the term as those do who 
imagine that there is a substantial form of a piece of stone, or of 
some other non-organic body ; for principles of life belong only to 
organic bodies. It is true... that there is no portion of matter in 

which there are not numberless organic and animated bodies But 

for all this, it must not be said that each portion of matter is 
animated, just as we do not say that a pond full of fish is an 
animated body, although a fish is so. 

G. VI. 543 (D. 167). Not only the soul, but also the same 

animal, subsists What does not begin to live, does not cease to 

live either; and death, like generation, is only the transformation 
of the same animal, which is sometimes increased, sometimes di- 
minished The machines of nature being machines even in their 

smallest parts, are indestructible, because of the envelopment of a 
small machine in a larger one ad infinitum. Thus we are obliged to 
maintain at the same time both the pre-existence of the soul as of 
the animal, and the substance of the animal as of the soul. 

G-. VII. 530 (D. 191). To each primitive entelechy or each 
vital principle there is perpetually united a certain natural machine, 
which comes to us under the name of organic body : which machine, 
although it preserves its form in general, consists in a fiux, and is, 
like the ship of Theseus, perpetually repaired. And we cannot be 
certain that the smallest particle received by us at birth remains 



270 SOUL AND BODY. 

in our body.... Some animal always remains, although no particular 
animal ought to be called everlasting. 

G. V. 214 (N. E. 240). Organization or configuration, without 
a subsistent principle of life, which I call a Monad, would not suffice 
for the continuance of idem numero, or the same individual; for 
configuration may remain specifically without remaining individu- 
ally.... Organized bodies, as well as others, remain the same only in 
appearance. ...But as for Substances, which have in them a true and 
real substantial unity..., and as for substantial beings, which... are 
animated by a certain indivisible spirit, it is right to say that 
they remain perfectly the same individual, through this soul or 
spirit, which makes the Ugo in those which think. 

G. III. 356. I have said, not absolutely, that organism is 
essential to matter, but to matter arranged by a sovereign wisdom. 

G. II. 100. I admit that the body apart, without the soul, has 
only a unity of aggregation, but the reality which remains to it 
comes from the parts which compose it, and which retain their 
substantial unity because of the numberless living bodies which are 
enveloped in them. However, though it is possible for a soul to have 
a body composed of parts animated by separate souls, the soul or 
form of the whole is not on that account composed of the souls or 
forms of the parts. 

G. VI. 619 (D. 229; L. 258). rt must not be imagined... 
that each soul has a quantity or portion of matter belonging exclu- 
sively to itself or attached to it for ever, and that it consequently 

owns other inferior living beings For all bodies are in a perpetual 

flux, like rivers There is often metamorphosis in animals, but 

never metempsychosis or transmigration of souls ; nor are there 
souls entirely separate or disembodied spirits. God alone is com- 
pletely without body. 

G. II. 58 (1686). Each [soul and body] following its laws, and 
one acting freely, the other without choice, agrees (se rencontre) in 
the same phenomena. The soul, however, is none the less the form 
of its body, because it expresses the phenomena of all other bodies 
according to their relation to its own. 

G. VI. 595. I should have been much mistaken if I had 
objected to the Cartesians that the agreement which, according to 
them, God maintains immediately between the soul and the body, 
does not make a veritable union, since assuredly my pre-established 

Harmony cannot do so either However I do not deny that there 

is something of this nature ; and this would be analogous to presence, 



SOUL AND BODY. 271 

of which hitherto, as applied to incorporeal things, the notion has 
not been sufficiently explained. 

G. VI. 598 (D. 209; L. 408). Each specially important 
simple substance or Monad, which forms the centre of a compound 
substance {e.g. of an animal) and the principle of its unity, is 
surrounded by a mass composed of an infinity of other Monads, 
which constitute the particular body of this central Monad.... This 
body is organic, when it forms a kind of automaton or natural 
machine, which is a machine not only as a whole, but also in the 
smallest parts of it that can come into observation. 

G. II. 306. It is not to be thought that an infinitesimal 
portion of matter is to be assigned to each entelechy ; there is no 
such piece. 

G. II. 378. Although there is no absolute necessity for every 
organic body to be animated, yet we must judge that God would 
not have neglected the opportunity for a soul, since his wisdom 
produces as much perfection as it can. 

G. III. 363. Simple substance... cannot have extension in it, 
for all extension is composite. 

G. VII. 468. Our substantial matter has only potential parts, 
but the human body is an aggregate. 



XII. § 91. Second theory of Soul and Body. 

G. III. 657 (D. 234). -A. true substance (such as an animal) is 
composed of an immaterial soul and an organic body, and it is the 
compound of these two which is called unum per se. 

G. IV. 391 (D. 63). Just as all things are full of souls, so 
also they are full of organized bodies. 

G. V. 309 (N. E. 362). Perfect unity must be reserved for 
bodies which are animated, or endowed with primitive entelechies. 

G. II. 75 (1686). Our body in itself, apart from the soul,... 
can only be called one substance improperly, like a machine or a 
heap of stones. 

Q, II, 77 (1686). If I am asked, in particular, what I say of 
the sun, the globe of the earth, the moon, trees and similar bodies, 
and even beasts, I could not affirm absolutely that they are 
animated, or at least that they are substances, or whether they are 
merely machines or aggregates of several substances. But at least I 
can say that if there are no corporeal substances such as I want, it 
follows that bodies will be only true phenomena, like the rainbow. . . . 



272 SOUL AND BODY. 

We shall never come to anything of which we can say: "there is 
truly a being,'' except when we find animated machines to which 
their soul or substantial form gives a substantial unity independent 
of the external union of contact. And if there are none such, it 
follows that except man there would be nothing substantial in the 
visible world. 

G. II. 371. I do not deny a certain reed metaphysical union 
between the soul and the organic body..., according to which it 

could be said, that the soul really is in the body But you see 

that I have been speaking, not of the union of the Entelechy or 
active principle with materia prima or passive power, but of the 
union of the soul, or the Monad itself (resulting from both prin- 
ciples) with mass or with other monads. 

G. VII. 502. Every created monad is provided with some 

organic body Every mass contains innumerable monads, for 

although every organic body in nature has its corresponding monad, 
yet it contains in its parts other monads similarly provided with their 
organic bodies, which are subservient to the primary organic body. 

G. IV. 511 (D. 120). So far as by its union with matter [the 
substantial form] constitutes a substance truly one, or a thing that 
is one per se, it forms what I call a monad. 

G. II. 118. As for the other difficulty which you [Arnauld] 
make. Sir, namely that the soul joined to matter does not make a 
being truly one, since matter is not truly one in itself, and the soul, 
as you judge, gives it only an extrinsic denomination, I answer that 
it is the animated substance, to which this matter belangs, which is 
truly one being, and matter taken as mere mass is only a pure 
phenomenon or well-founded appearance. 

G. II. 120. -A. whole which has a true unity can remain the 
same individual, strictly speaking, though it gains or loses parts, as 
we experience in ourselves. 

G. II. 368. A new entelechy can be created, even if no new 
part of mass is created ; for although mass already has unities 
everywhere, yet it is always capable of new ones, dominating many 
others ; as if you were to imagine that God should make an organic 
body out of a mass which, as a whole, is inorganic, e.g. a lump of 
stone, and should set its soul over itj for there are as many 
entelechies as there are organic bodies. 

G. II. 370. Every part of an organic body contains other 
entelechies. 

G. II. 304i A fraction or half of an animal is not one Being 



SOUL AND BODY. 273 

•per se, because this can only be understood of the animal's body, 
which is not one being per se, but an aggregate, and has an arith- 
metical, but not a metaphysical unity. 

G. II. 251. A primitive entelechy can never arise or be extin- 
guished naturally, and can never be without an organic body. 



XII. § 92. The vinculum substantiale. 

G. II. 399. Since the bread is really not a substance, but a 
being by aggregation or a suhstantiatum, resulting from innumerable 
monads by a certain superadded union, its substantiality consists in 
this union ; thus it is not necessary according to you [the Catholics] 
that God should abolish or change those monads, but only that he 
should take away that by means of which they produce a new being, 
namely this union ; thus the substantiality which consists in it will 
cease, though the phenomenon will remain, arising now not from those 
monads, but from some divine equivalent substituted for the union 
of those monads. Thus there will really be no substantial subject 
present. But we, who reject transubstantiation, have no need of 
such theories. [This passage precedes the first suggestion of the 
vinculum substantiale.^ 

G. II. 435. We must say one of two things : either bodies are 
mere phenomena, and thus extension also is nothing but a pheno- 
menon, monads alone are real, and the union is supplied by the 
operation of the percipient soul in the phenomenon ; or, if faith 
leads us to corporeal substances, this substance will consist in 
the reality of the union, which adds something absolute (and therefore 
substantial), though temporary, to the monads which are to be 
united. ...If this substantial bond of monads were absent, all bodies 
with all their qualities would be only well-founded phenomena. 

G. II. 461. Supernatural matters being opposed to philosophy, 
we need nothing else than monads and their internal modifications. 

G. II. 481. I have changed my mind, so that I think nothing 
absurd will follow if we hold the vinculum substantiale also... to be 
ingenerable and incorruptible ; since indeed I think no corporeal 
substance should be admitted except where there is an organic body 

with a dominant monad Since, "therefore, I deny... not only that 

the soul, but also that the animal can perish, I shall say that the 
vinculum substantiale also... cannot arise or cease naturally. 

G. II. 516. This vinculum substantiale is naturally, but not 
essentially, a bond. For it requires monads, but does not essentially 

R. L. 18 



274 SOTIL AND BODY. 

involve them, since it can exist without monads, and monads 
without it. 

G. II. 517. If monads alone were substances, it would be 
necessary either that bodies should be mere phenomena, or that the 
continuum should arise out of points, which is certainly absurd. 
Real continuity cannot arise except from the vinculum mhstantiale. . 

G. II. 520. Monads alone do not compose the continuum, 
since per se they are destitute of all connection, and each monad is 
like a world apart. But in materia prima (for materia secunda is an 
aggregate), or in the passive element of a composite substance, is 
involved the foundation of continuity, whence the true continuum 

springs from juxtaposed compound substances And in this sense 

I may perhaps have said that extension is a modification of materia 
prima, or of what is formally non-extended. 



XII. I 94. Preformation. 

G. VII. 531 (D. 192). I hold that the souls, latent in 
seminal animalcules from the beginning of things, are not rational 
until, by conception, they are destined for human life; but when 
they are once made rational and rendered capable of consciousness 
and of society with God, I think that they never lay aside the 

character of citizens in the Republic of God Death... can render 

perceptions confused, but cannot entirely blot them from memory, 
the use of which returning, rewards and punishments take place. 

Cr, VI. 152. I hold that souls, and simple substances generally, 
can only begin by creation, and end by annihilation : and as the 
formation of animated organic bodies does not seem explicable in the 
order of nature, unless we suppose an already organic preformation, 
I have hence inferred that what we call the generation of an animal 
is only a transformation and augmentation : thus since the same 
body was already organized, it is to be believed that it was 

already animated, and that it had the same soul I should believe 

that souls which will one day be human, like those of the other 
species, have been in the seeds, and in the ancestors up to Adam, 
and have consequently existed since the beginning of things, always in 

a sort of organized body But it seems proper, for several reasons, 

that they should have existed then only as sensitive or animal souls. . . 
and that they remained in that state until the time of the generation 
of the man to whom they were to belong, but that then they received 
reason, whether there be a natural method of elevating a sensitive 



CONFUSED AND UNCONSCIOUS PERCEPTION. 275 

soul to the degree of a reasonable soul (which I have difficulty in 
conceiving), or that God gave reason to this soul by a special opera- 
tion, or (if you will) by a kind of transcreation. 

G. VI. 352. I should prefer to do without miracle in the 
generation of man, as of the other animals; and this could be 
explained by conceiving that, among the great number of Souls and 
Animals, or at least of organic living bodies, which are in the seed, 
those souls alone which are destined to attain some day to human 
nature contain the reason which will some day appear in them. 

G. Ill, 565. The question always remains whether the basis of 
the transformation, or the preformed living being, is in the ovary... 
or the sperm. ...For I hold that there must always be a preformed 
living being, whether plant or animal, which is the basis of the 
transformation, and that it must contain the same dominant 
monad. 

G. VI. 543 (D. 167). I am of the opinion of Mr Cudworth... 
that the laws of mechanism alone could not form an animal, where 
there is as yet nothing organized. 



XIII. § 96. Unconscious mental states. 

G. V. 107 (N. E. 118). What is noticeable must be composed 

of parts which are not so It is impossible for us to think expressly 

upon all our thoughts ; otherwise, the mind would reflect upon each 
reflection to infinity, without ever being able to pass to a new thought. 

G. V. 109 (N. E. 120). These sense-ideas [heat, softness, cold] 
are simple in appearance, because, being confused, they do not give 
the mind the means of distinguishing their contents. 

G. V. 48 (N. E. 49 ; L. 373). These insensible perceptions 
also mark and constitute the same individual, who is characterized 
by traces or expressions, which they preserve, of the preceding states 
of this individual.... It is also by the insensible perceptions that we 
explain that admirable pre-established Harmony of the soul and the 
body, and even of all monads. 

G. V. 49 (N. E. 51 ; L. 377). I have also noticed that, in 
virtue of insensible variations, two individual things cannot be 
perfectly alike, and that they must always dififer more than numeri- 
cally. 

G. V. 79 (S. E. 84). PhUahthes [Locke] : It is very difficult 
to conceive that a truth should be in the mind, if the mind has. 
never thought of this truth. Theophilus [Leibniz] :...This reasoning 

18—2 



276 Leibniz's theory of knowledge. 

proves too much ; for if truths are thoughts, we shall be deprived, 
not only of truths of which we have never thought, but also of those 
we have thought of, but are no longer actually thinking of; and 
if truths are not thoughts, but habits and aptitudes, natural or 
acquired, nothing hinders there being some in us of which we never 
have thought and never will think. 

Gr. V. 148 (N. E. 166). We have always an infinity of minute 
perceptions without perceiving them. We are never without 
perceptions, but it is necessary that we should be often without 
apperceptions, namely when there are no perceptions which are 
noticed \distvnguees\ 

G. V. 97 (N. E. 105). In order that knowledge, ideas or truths 
should be in our mind, it is not necessary that we should have ever 
actually thought of them ; they are only natural habits, that is to 
say, active and passive dispositions and attitudes, and more than a 
tabula rasa. 



XIV. § 99. Innate ideas and truths. 

G. V. 70 (N. E. 75). I agree that we learn innate ideas and 
truths, whether by attending to their source, or by verifying them 
through experience. Thus I do not make the supposition you 
[Locke] suppose, as if, in the case of which you speak, we learnt 
nothing new. And I cannot admit this proposition : Whatever we 
learn is not innate. 

G. V. 71 (N. E. 76). Ph. : Is it not possible that not only the 
terms or words which we use, but also the ideas, come to us from 
without ? 2'h. : It would then be necessary that we should ourselves 
be outside of ourselves, for intellectual ideas, or ideas of reflection, 
are drawn from our mind : And I should much like to know how 
we could have the idea of being, if we were not ourselves Beings, 
and did not thus find being in us ? 

G. V. 76 (N. E. 80). If [the mind] had only the mere capacity 
for receiving knowledge... it would not be the source of necessary 
truths, as I have just shown that it is ; for it is incontestable that 
the senses do not suffice for showing their necessity. 

G. V. 79 (N. E. 84). The proposition, the sweet is not the bitter, 
is not innate, according to the sense we have given to the term 
innate truth. For the feelings of sweet and bitter come from the 
external senses. ... But as for the proposition, the square is not a 
circle, we may say that it is innate, for, in considering it, we make a 



LEIBNIZ'S THEORY OF KNOWLEDGE. 277 

subsumption or application of the principle of contradiction to what 
the understanding itself furnishes. 

G. V. 100 (N. E. 111). I shall be opposed by this axiom, 
admitted among philosophers, that nothing is in the soul which does 
not come from the senses. But we must except the soul itself and 
its affections. Nihil est in intellectu, quod non fuerit m sensu, 
excipe : nisi ipse intellectus. Now the soul contains being, substance, 
unity, identity, cause, perception, reasoning, and many other notions, 
which the senses cannot give. 

G. V. 139 (N, E, 156), A succession of perceptions awakes in 
us the idea of duration, but does not create it. 

G. V. 279 (N. E. 325). [Ideas] express only possibilities; 
thus, if there had never been a parricide,... parricide would be a 
possible crime, and its idea would be real. 

G. V. 324 (N. E. 380). The purpose of the predicaments is very 
useful, and we ought to think rather of rectifying than of rejecting 
them. Substances, quantities, qualities, actions or passions, and 
relations... may suffice, with those formed by their composition. 

G. V. 338 (N. E. 400). It is quite true that truth is always 
founded in the agreement or disagreement of ideas, but it is not true 
generally that our knowledge of truth is a perception of this agree- 
ment or disagreement. 

G. V. 347 (N. E. 410). As for the primitive truths of fact, 
they are immediate internal experiences of an immediacy of feeling. 
And it is here that the first truth of the Cartesians or of St. 
Augustine occurs : / think, therefore I am, i.e. / am a thing which 
thinks. But... it is not only immediately clear to me that / think, 
but it is just as clear to me that / hive different thoughts. . . .Thus the 
Cartesian principle is sound, but is not the only one of its kind. 

G. V. 391 (N. E. 469). We may always say that the proposi- 
tion I exist is of the highest evidence, being a proposition which 
cannot be proved by any other, or an immediate truth. And to say : 
I think, therefore lam, is not properly to prove existence by thought, 
for to think and to be thinking are the same thing ; and to say / am 
* thinking is already to say / am. You may, however, with some 
reason, exclude this proposition from among the Axioms, for it is 
a proposition of fact, founded on an immediate experience, and not 
a necessary proposition, whose necessity is seen in the immediate 
agreement (comoenance) of the ideas. On the contrary, only God 
sees how these two terms, I and Existence, are connected, i.e. why 
I exist. 



278 LEIBNIZ'S THEORY OF KNOWLEDGE. 

G. V. 415 (N. E. 499). The immediate apperception of our 
existence and of our thoughts furnishes us the first d, posteriori 
truths or truths of fact, i.e. the first experiences, as identical proposi- 
tions contain the first & priori truths or truths of reason. . . . Both are 
incapable of being proved, and may be called immediate ; the former, 
because there is immediacy between the understanding and its 
object, the latter, because there is immediacy between the subject 
and the predicate. 

G. VII. 263 (N. E. 716). By the word idea we understand 
something which is in our mind; therefore marks impressed upon 
the brain are not ideas. ...But many things are in our minds— e.gr. 
thoughts, perceptions, affections — which we recognize not to be 
ideas, though they cannot occur without ideas. For an idea does not 
consist for us in any act of thought, hut in a faculty — There is 
nevertheless, in this also, a certain difficulty ; for we have a remote 
faculty of thinking about all things, even those whose ideas we are 
perhaps destitute of, because we have the faculty of receiving them ; 
therefore an idea demands some nea/r faculty or facility of thinking of 

a thing. But even this does not suffice It is therefore necessary 

that there should be something in me which not only leads to the 
thing, hut also expresses it. [See XI. § 75.] 

G. IV. 357 (D. 48). The first of the truths of reason is the 

principle of contradiction The first truths of fact are as many as 

the immediate perceptions. 

G. V. 15 (D. 95; N. E. 15). As for the question whether 
there are ideas and truths born with us, I do not find it absolutely 
necessary for the beginnings, nor for the practice of the art of 
thinking, to decide it.... The question of the origin of our ideas and 
maxims is not preliminary in philosophy ; and we must have made 
great progress to solve it well. 

G. VI. 505 (D. 155). Since the senses and inductions can 
never teach us perfectly universal truths, nor what is absolutely 
necessary, but only what is, and what is found in particular ex- 
amples, and since we nevertheless know necessary and universal 
truths... it follows that we have derived these truths in part from 
what is within us. 

G. II. 121. I agree that the idea we have of thought is clear, 
but not everything clear is distinct. ...It is an abuse to wish to 
employ confused ideas, however clear, to prove that something 
cannot be. 

G. III. 479. The soul is innate to itself, so to speak, and 



LEIBNIZ'S THEORY OF KNOWLEDGE. 279 

consequently existence, substance, unity, sameness, diversity, etc.,... 
are so also. 

G. V. 156 (N. E. 175). Ph. -. Bodies do not furnish us by 
means of the senses with so clear and distinct an idea of active 
power as that which we have of it by the reflections which we make 

on the operations of our mind Th. : These considerations are very 

good. 

G. V. 340 (N. E, 402). Since all belief consists in memory of 
past life, of proofs or of reasons, it is not in our power or in our free 
will to believe or not to believe, since memory is not a thing which 
depends on our will. 

G. V. 66 (N. E. 70). I have always been, as I still am, in 
favour of the innate idea of God... and consequently of other innate 
ideas, which cannot come to us from the senses. Now I go still 
further, in conformity to the new system, and I even think that all 
the thoughts arid actions of our soul come from its own nature, and 

that it is impossible they should be given to it by the senses But 

at present I will set aside this investigation, and accommodating 
myself to the received expressions, ...I shall examine how we ought 
to say, in my opinion, even in the usual system (speaking of the 
action of bodies on the soul, as the Copernicans, like other men, 
speak, with good foundation, of the motion of the sun) that there 
are ideas and principles which do not come to us from the senses, 
which we find in us without forming them, though the senses give 
us occasion to notice them. 

G. III. 659. There is no necessity (it seems) to take [ideas] as 
something which is outside us. It is sufficient to consider ideas as 
notions, i.e. as modifications of our soul. 

XIV. § 102. Distinction of sense and intellect. 

Q.^ JY_ 436 (1686). It can even be proved that the notion of 
magnitude, of figure and of motion, is not so distinct as is supposed, 
and that it involves something imaginary and relative to our per- 
' ceptions, as do also (though far more) colour, heat, and other similar 
qualities, concerning which we may doubt whether they really are 
found in the nature of things external to us. 

G. V. 77 (N. E. 82). The intellectual ideas which are the 
source of necessary truths do not come from the senses. ...The ideas 
which come from the senses are confused, and the truths which 
depend upon them are so also, at least in part; whereas the intellec- 



280 LEIBNIZ'S THEORY OF KNOWLEDGE. 

tual ideas and the truths which depend upon them are distinct, and 
neither have their origin in the senses, though it is true we should 
never think without the senses. 

G. V. 108 (N. E. 119). I distinguish between ideas and 
thoughts ; for we always have all pure or distinct ideas independently 
of the senses ; but thoughts always correspond to some sensation. 

Q^ Y. 117 (H'. E. 130). It seems that the senses cannot 
convince us of the existence of sensible things without the aid 
of reason. Thus I should hold that the consideration of existence 
comes from reflection. 

G. V. 197 (N. E. 220). The senses provide us with the matter 
for reflections, and we should never even think of thought, if we did 
not think of something else, i.e. of the particulars which the senses 
provide. 

G. V. 220 (N. E. 248). Present or immediate memory, or 
the recollection of what has just happened, i.e. the consciousness 
or reflection which accompanies internal action, cannot naturally 
deceive ; otherwise we should not even be sure that we are thinking 

of such and such a thing If immediate internal experiences are 

not certain, there will be no truth of fact of which we can 
be sure. 

G. V. 363 (N. E. 432). The ideas of sensible qualities are 
confused, and the powers, which ought to produce them, consequently 
also furnish only ideas in which there is an element of confusion ; 
thus we cannot know the connections of these ideas otherwise than 
by experience, except in so far as they are reduced to distinct ideas 
which accompany them, as has been done (for example) in regard to 
the colours of the rainbow and prisms. 

G. V. 373 (N. E. 445). Our certainty would be small, or 
rather nothing, if it had no other foundation for simple ideas but 
that which comes from the senses. ...Ideas are originally in our 
mind, and even our thoughts spring from our own nature, without 
the other creatures being able to have an immediate influence on the 
soul. Moreover the foundation of our certainty in regard to universal 
and eternal truths is in the ideas themselves, independently of the 
senses, as also pure and intelligible ideas do not depend upon the 

senses But the ideas of sensible qualities... (which in fact are only 

phantoms) come to us from the senses, i.e. from our confused percep- 
tions. And the foundation of the truth of contingent and particular 
things is in success, which shows that the phenomena of sense are 
connected rightly, as the intelligible truths demand. 



LEIBNIZ S THEORY OF KNOWLEDGE. 281 

G. VI. 499 (D. 149). We may say that sensible qualities are 
in fact occult qualities, and that there must certainly be others more 
manifest, which could make them explicable. And far from our 
understanding only sensible things, they are just what we under- 
stand least. 

G. VI. 500 (D. 150). However, we must do the senses this 
justice, that besides these occult qualities, they make us know other 
more manifest qualities, which furnish more distinct notions. These 
are those attributed to common sense, because there is no external 

sense to which they are specially attached and peculiar Such is 

the idea of numbers It is thus also that we perceive figures 

Though it is true that, to conceive numbers and figures themselves 
distinctly, ...we must come to things which the senses cannot 
furnish, and which the understanding adds to the senses. 

G. VI. 502 (D. 152). There are therefore three classes of 
notions : those which are sensible only, which are the objects appro- 
priated to each particular sense, those which are at once sensible and 
intelligible, which belong to common sense, and those which are 
intelligible only, which are peculiar to the understanding. 

G. I. 352. The mark of imperfect knowledge, for me, is when 
the subject has properties of which we cannot yet give the proof. 
Thus geometers, who have not yet been able to prove the properties 
of the straight line, which they have taken as acknowledged, have 
not yet had a sufficiently distinct idea of it. 

G. II, 412. Would that incomprehensibility were an attribute 
of God only ! We should then have better hope of understanding 
nature. But it is too true that there is no part of nature which 

we can perfectly understand No creature however noble can 

distinctly perceive or comprehend an infinity at one time ; nay 
more, whoever understood one piece of matter, would understand 
the whole universe. 



XIV. § 103. The quality of ideas. 

G. V. 243 (N. E, 273). I have this idea [a distinct one] of 
it [a chiliagon], but I cannot have the image of a chiliagon. 

G. II. 265. The ways of action of the mind, you say, are 
more obscure. I should have thought they were the clearest, and 
were almost alone clear and distinct. 

G. V. 472 (N. E. 574). God alone has the advantage of 
having only intuitive knowledge. 



282 LEIBNIZ'S THEORY OF KNOWLEDGE. 

XIV. § 104. Definition. 

G. V. 248 (N. E. 279). When there is only an incomplete 
idea, the same subject is susceptible of several mutually independent 
definitions, so that we cannot always derive the one from the other, 
...and then only experience teaches us that they all belong to it 
together. 

G. V. 274 (N. E. 317). The real [definition] shows the 
possibility of the thing defined, and the nominal definition does not 
do so. 

G. V. 275 (N. E. 319). Simple terms cannot have a nominal 
definition : but... when they are simple only in relation to us (because 
we have not- the means of analyzing them in order to reach the 
elementary perceptions of which they are composed), like hot, cold, 
yellow, green, they can receive a real definition, which will explain 
their cause. 

G. V. 300 (N. E. 353). When the question is concerning 
fictions and the possibility of things, the transitions from species to 

species may be insensible This indeterminateness would be true 

even if we knew perfectly the interior of the creatures concerned. 
But I do not see that it could prevent things from having real 
essences independently of the understanding, or us from knowing 
them. 

G. IV. 424 (D. 30) (1684). We have a distinction between 
nominal definitions, which only contain the marks of the thing 
which is to be distinguished from others, and real definitions, from 
which it appears that the thing is possible ; and by this Hobbes is 
answered, who held truths to be arbitrary, because they depended on 
nominal definitions, not considering that the reality of the definition 
is not arbitrary, and that not any notions can be conjoined. 

G. IV. 450 (1686). When [definition] pushes analysis until it 
reaches primitive notions, without presupposing anything whose 
possibility requires an cb priori proof, the definition is perfect or 



XIV. § 105. The Characteristica Universalis. 

G. V. 460 (N. E. 559). I hold that the invention of the form 
of syllogisms is one of the most beautiful which the human mind has 
made, and even one of the most considerable. It is a kind of 
tmiverscd mathematics whose importance is not sufficiently known. 



Leibniz's theoky of knowledge. 283 

G. V. 461 (N. E. 560). Further it should be known that there 
aro good asyllogistie conclusions... e.g.: Jesus Christ is God, therefore 
the mother of Jesus Christ is the mother of God... If David is the 
father of Solomon, without doubt Solomon is the son of David. And 
these consequences do not fail to be demonstrable by truths upon 
which common syllogisms themselves depend. 

G. I. 67 (ca. 1672). In Philosophy, I have found a means of 
accomplishing in all sciences what Des Cartes and others have done 
in Arithmetic and Geometry by Algebra and Analysis, by the Ars 

Combinaioria By this all composite notions in the whole world 

are reduced to a few simple ones as their Alphabet; and by the 
combination of such an alphabet a way is made of finding, in time, 
by an ordered method, all things with tjieir theorems and whatever 
is possible to investigate concerning them. 

G. III. 216. I had considered this matter. ..when I was a 
young man of nineteen, in my little book de Arte Combinaioria, and 
my opinion is that truly real and philosophic characters must corre- 
spond to the analysis of thoughts. It is true that these characters 
would presuppose the true philosophy, and it is only now that I 
should dare to undertake their construction. 

G. M. II. 104. What is best and most convenient about my 
new calculus [the infinitesimal calculus] is, that it ofiers truths 
by a kind of analysis, and without any efibrt of imagination, which 
often only succeeds by chance, and that it gives us over Archimedes 
all the advantages which Vieta and Des Cartes had given us over 
Apollonius. 

Q._ VII, 185. [In 3,n account of a boyish speculation Leibniz 
says] I came upon this remarkable consideration, namely, that a 
certain Alphabet of human thoughts could be invented, and that 
from the combination of the letters of this alphabet, and from the 
analysis of the words formed of them, everything could be both 
discovered and tested. ...At that time I did not sufficiently realize 
the greatness of the matter. But later, the more progress I made 
in the knowledge of things, the more confirmed I became in the 
resolve to pursue so great a matter. 

Q., VII. 20. Algebra itself is not the true characteristic of 
Geometry, but quite another must be found, which I am certain 
would be more useful than Algebra for the use of Geometry in the 
mechanical sciences. And I wonder that this has hitherto been 
remarked by no one. For almost all men hold Algebra to be the 
true mathematical art of discovery, and as long as they labour 



284 PROOFS OF THE EXISTENCE OF GOD. 

under this prejudice, they will never find the true characters of the 
other sciences. 

G. VII. 198. The progress of the art of rational discovery 
depends in great part upon the art of characteristic {ars character- 
istica). The reason why people usually seek demonstrations only 
in numbers and lines and things represented by these is none 
other than that there are not, outside numbers, convenient cha- 
racters corresponding to the notions. 

XV. § 106. Four proofs of the escistence of Ood. 

G. VII. 302 (D. 100; L. 337). Besides the world or the 
aggregate of finite things, there is a certain unity which is dominant, 
not only as the soul is dominant in me, or rather as the Ego itself 
is dominant in my body, but also in a much higher sense. For the 
dominant unity of the universe not only rules the world but 
constructs or fashions it. It is higher than the world, and so to 
speak extramundane, and is indteed the ultimate reason of things. 
For the sufficient reason of existence cannot be found either in any 
particular thing or in the whole aggregate and series of things. 
Let us suppose that a book of the elements of Geometry existed 
from all eternity, and that in succession one copy of it was made 
from another, it is evident that, although we can account for the 
present book by the book from which it was copied, nevertheless, 
going back through as many books as we please, we could never 
reach a complete reason for it, because we can always ask why such 
books have at all times existed, i.e. why books at all, and why 
written in this way. What is true of books is also true of the 
difierent states of the world ; for, in spite of certain laws of change, 
the succeeding state is, in some sort, a copy of that which precedes 
it. Therefore, to whatever earlier state you go back, you never 
find in it the complete reason of things, i.e. the reason why there 
exists any world, and why this world rather than some other. 

You may indeed suppose the world eternal ; but as you suppose 
only a succession of states, in none of which do you find the 
sufficient reason, and as even any number of them does not in the 
least help you to account for them, it is evident that the reason 
must be sought elsewhere. For in eternal things, even though 
there be no cause, there must be a reason, which, for permanent 
things, is necessity itself or essence ; but for the series of changing 
things, if it be supposed that they succeed one another from all 



PROOFS OF THE EXISTENCE OF GOD. 285 

eternity, this reason would be, as we shall presently see, the prevail- 
ing of inclinations, which consist not in necessitating reasons. . .but in 
inclining reasons. From this it is manifest that, even by supposing 
the eternity of the world, we cannot escape the ultimate extra- 
mundane reason of things, i.e. God.... Since the ultimate root of all 
must be in something which has metaphysical necessity, and since 
the reason of any existing thing is to be found only in an existing 
thing, it follows that there must exist one Being who has meta- 
physical necessity, one Being of whose essence it is to exist ; and 
thus there must exist something diflferent from that plurality of 
beings, the world, which, as we admitted and showed, has no meta- 
physical necessity. 

G. VI. 614 (D. 224 ; L. 241). In God is the source, not only 
of existences, but also of essences in so far as they are real, i.e. the 
source of what is real in possibility. For the understanding of 
God is the region of eternal truths, or of the ideas on which they 
depend, and without him there would be nothing real in possi- 
bilities, and not only would there be nothing existing, but nothing 
would even be possible. For if there is a reality in essences or 
possibilities, or in eternal truths, this reality must needs be founded 
in something existing and actual, and consequently in the exist- 
ence of the necessary Being, in whom essence involves existence, 
or in whom it suffices to be possible in order to be actual. Thus 
God alone (or the necessary Being) has this prerogative, that he 
must necessarily exist if he be possible. And as nothing can 
interfere with the possibility of that which involves no limits, no 
negation, and consequently no contradiction, this is sufficient of 
itself to make known the existence of God a priori. We have 
proved it also through the reality of eternal truths.... We must not, 
however, imagine, as some do, that eternal truths, being dependent 

upon God, are arbitrary and depend upon his will That is only 

true of contingent truths, whose principle is fitness or the choice of 
the best, whereas necessary truths depend solely on his understanding, 
and are its internal object. Thus God alone is the primary unity 
or original simple substance, of which all created or derivative 
Monads are products, and have their birth, so to speak, through 
continual fulgurations of the Divinity from moment to moment, 
limited by the receptivity of the created being, of whose essence it 
is to have limits. In God there is Power, which is the source of all, 
then Knowledge, whose content is the variety of ideas, and finally 
Will, which makes changes or products according to the principle 



286 PROOFS OF THE EXISTENCE OF GOD. 

of the best. These characteristics correspond to what in created 
monads forms the subject or basis [see Mr Latta's note, L. 245], to 
the faculty of Perception, and to the faculty of Appetition. But in 
God these attributes are absolutely infinite or perfect ; and in the 
created Monads... there are only imitations of these , attributes, 
according to the degree of perfection of the Monad. 



XV. § 107. The ontological argument. 

G. V. 419 (N. E. 504). [The ontological argument] is not a 
paralogism, but an imperfect demonstration, which presupposes 
something that it was still necessary to prove, to give the argument 
mathematical evidence ; namely, it is tacitly supposed that this idea 
of the all-great or all-perfect Being is possible, and implies no 
contradiction. And it is already something that, by this remark, 
it is proved that supposing God to he possible, he exists, which is the 
privilege of the Divinity alone.... The other argument of M. Des 
Cartes — which undertakes to prove the Existence of God, because 
the idea of him is in our soul, and must have come from the original 
— is still less conclusive. 

G. V. 420 (N. E. 505). Almost all the means which have 
been employed for proving the existence of God are good, and might 
serve their purpose if they were perfected. 

G. IV. 406 (D. 137). If the necessary Being is possible, he 
exists. For the necessary Being and the Being by his essence are 
one and the same thing. ...If the Being through self is impossible, 
all beings through others are so too, since they only are, in the end, 
through the Being through self; and thus nothing could exist.... If 
there is no necessary Being, there is no possible being. 

G. III. 672. I agree that the idea of possibles involves neces- 
sarily that {i.e. the idea) of the existence of a being who can produce 
the possible. But the idea of possibles does not involve the actual 
existence of this being, as it seems. Sir, that you take it, when you 
add : " If there were not such a being, nothing would be possible." 
For it suffices that a being who would produce the thing should be 
possible, in order that the thing should be possible. Generally 
speaking, in order that a being may be possible, it suffices that its 
efficient cause be possible ; I except the supreme efficient cause, 
which must actually exist. But this is for another reason, because 
nothing would be possible if the necessary Being did not exist. 



PROOFS OF THE EXISTENCE OF GOD. 287 

XV. § 108. Proof that the idea of God is possible. 

Gf. VII. 261 (N. E. 714) (1676). That the most perfect Being 
exists. I call a perfection every simple quality which is positive 
and absolute, and expresses without any limits whatever it does 
express. Now since such a quality is simple, it is also irresolvable 
or indefinable, for otherwise it will either not be one simple quality, 
but an aggregate of several, or, if it is one, it will be circumscribed 
by limits, and will therefore be conceived by a negation of further 
progress, contrary to the hypothesis, for it is assumed to be purely 
positive. Hence it is not difficult to show that all perfections are 
compatible inter se, or can be in the same subject. For let there 
be such a proposition as 

A and £ are incompatible 
(understanding by A and £ two such simple forms or perfections — 
the same holds if several are assumed at once), it is obvious that this 
cannot be proved without a resolution of one or both of the terms 
A and £; for otherwise their nature would not enter into the 
reasoning, and the incompatibility of any other things could be 
shown just as well as theirs. But (by hypothesis) they are irre- 
solvable. Therefore this proposition cannot be proved concerning 
them. 

But it could be proved concerning them if it were true, for it 
is not true per se ; but all necessarily true propositions are either 
demonstrable, or known per se. Therefore this proposition is not 
necessarily true. In other words, since it is not necessary that A 
and £ should not be in the same subject, they can therefore be in 
the same subject; and since the reasoning is the same as regards 
any other assumed qualities of the same kind, therefore all perfec- 
tions are compatible. 

There is, therefore, or there can be conceived, a subject of all 
perfections, or most perfect Being. 

Whence it follows also that he exists, for existence is among the 
number of the perfections. . . . 

I showed this reasoning to D. Spinoza, when I was at the Hague, 
and he thought it sound ; for as at first he contradicted it, I wrote 
it down and read him this paper. 

SCHOLIUM. 
The reasoning of Des Cartes concerning the existence of the 
most perfect Being presupposed that the most perfect Being can be 



288 PROOFS OF THE EXISTENCE OF GOD. 

conceived, or is possible. . . . But it is asked whether it is in our power 
to imagine such a Being. . . . 



XV. § 109. The cosmological argument. 

G. V. 417 (N. E. 500). [Locke argues that, because we now 
exist, therefore something has always existed. Leibniz replies :] 
I find ambiguity in it [your argument] if it means that tJiere never 
was a time when nothing existed. I agree to this, and indeed it 
follows from the preceding propositions by a purely mathematical 
consequence. For if there had ever been nothing, there would have 
always been nothing, since nothing cannot produce a Being ; conse- 
quently we ourselves should not be, which is contrary to the first 
truth of experience. But the consequence makes it first appear 
that in saying something has existed from all eternity, you mean an 
eternal thing. It does not follow, however, in virtue of what you 
have advanced so far, that if there has always been something, then 
there has always been a certain thing, i.e. an eternal Being. For 
some adversaries will say that I have been produced by other things, 
and these things by yet others, 

G. IV. 359 (D. 51). That there is some necessary thing is 
evident from the fact that contingent things exist. 

G. IV. 360 (D. 51). From the fact that we now are, it follows 
that we shall be hereafter, unless a reason of change exists. So 
that, unless it were established otherwise that we could not even 
exist except by the favour of God, nothing would be proved in 
favour of the existence of God from our duration. 



XV. § 111. The argument from the eternal truths. 

G. VII. 310. A necessary being, if it be possible^ exists. This 
. . .makes the transition from essences to existences, from hypothetical 
to absolute truths, from ideas to the world. ... If there were no eternal 
substance, there would be no eternal truths; thus God is also deduced 
hence, who is the root of possibility, for his mind is itself the region 
of ideas or truths. But it is very erroneous to suppose that eternal 
truths and the goodness of things depend on the divine will, since 
all will presupposes the judgment of the intellect as to goodness, 
unless some one by a change of names would transfer all judgment 
from the intellect to the will, though even then no one could say 
that the will is the cause of truths, since the judgment is not their 



PROOFS OF THE EXISTENCE OF GOD. 289 

cause either. The reason, of truths lies in the ideas of things, which 
are involved in the divine essence itself. And who would dare to 
say that the truth of God's existence depends upon the divine will ? 

G. VI. 226. We ought not to say, with some Scotists, that 
the eternal truths would subsist, even if there were no under- 
standing, not even God's. For, in my opinion, it is the divine 
understanding that makes the reality of eternal truths : although 
his Will has no part in it. Every reality must be founded in some- 
thing existent. It is true that an atheist may be a geometer. But 
if there were no God, there would be no object of Geometry. And 
without God, not only would there be nothing existent, but there 
would be nothing possible. 

G. VII. 190 (1677). A. You hold that this [a certain pro- 
position of Geometry] is true, even though it be not thought by you ? 
B. Certainly, before either the geometers had proved it, or men 
had observed it. A. Therefore you think that truth and false- 
hood are in things, not in thoughts? B. Certainly. A. Is 
anything false? B. Not the thing, I think, but the thought or 
proposition about the thing. A. Thus falsity belongs to thoughts, 
and not to things ? B. I am compelled to say so. A. Then is not 
truth also 1 B. It would seem so, though I doubt whether the 
consequence is valid. A. When the question is proposed, and before 
you are sure of your opinion, do you not doubt whether a thing 
is true or false ? B. Certainly. A. You recognize therefore that 
the same subject is capable of truth and falsehood, since one or 
other follows according to the nature of the question ? B. I recog- 
nize and affirm, that if falsity belongs to thoughts, not things, so 
does truth also. A. But this contradicts what you said above, 
that even what nobody thinks is true. B. You have puzzled me. 

A, Yet we must attempt a reconciliation. Do you think that 
all thoughts which can occur are actually formed, or, to speak 
more clearly, do you think that all propositions are thought ? 

B. I do not think so. A. You see then that truth concerns 
propositions or thoughts, but possible ones, so that this at least 
is certain, that if any one thinks in one way or in the opposite 
way, his thought will be true or false. [The rest of the dialogue is 
concerned in refuting Hobbes's nominalism.] 

XV. § 113. Relation of knowledge to truth. 

G. VI. 230. This pretended fate [that of the necessity of 
eternal truths], which governs even the divinity, is nothing else but 
R. L. 19 



290 PROOFS OF THE EXISTENCE OF GOD. 

the very nature of God, his own understanding, which furnishes 
rules to his wisdom and goodness. 

G. VI. 423. Is it by the will of God, for example, or is it not 
rather by the nature of numbers, that some numbers are more 
capable than others of being exactly divided in several ways ? 

G. II. 125. We may say that created spirits differ from God 
only as the less from the more, the finite from the infinite. 

G. IV. 426 (D. 32) (1684). As to the controversy, whether we 
see all things in God,... or have ideas of our own, it must be under- 
stood that, even if we did see all things in God, it would still be 
necessary that we should also have ideas of our own, i.e. not, as it 
were, certain little images, but affections or modifications of our 
mind, answering to what we should see in God. , 



XV. § 114. Argument from the pre-established harmony. 

G. V. 421 (N. E. 507). These Beings [Monads] have received 
their nature, both active and passive, . . . from a general and supreme 
cause, for otherwise, . . . being independent of each other, they could 
never produce that Order, Harmony, and Beauty, which is observed 
in nature. But this argument, which appears to have only a moral 
certainty, is brought to a perfectly metaphysical necessity, by the 
new species of harmony which I have introduced, which is the pre- 
established harmony. 

P. de C. 70 (D. 184). God produces substances, but not their 
actions, in which he only concurs. 

G. VII. 365 (D. 245). God is not present to things by 
situation, but hy essence; his presence is manifested by his immediate 
operation. 

G. VI. 107. Power is concerned with Being, wisdom or under- 
standing with the true, and will with the good. 

G. VI. 167. [God's] goodness led him antecedently to create 
and produce all possible good ; but his wisdom made choice of it, 
and was the cause of his choosing the best consequently ; and finally 
his power gave him the means of actually executing the great design 
which he had formed. 

G. IV. 440 (1686). God alone (from whom all individuals 
continually emanate, and who sees the universe, not only as they 
see it, but also quite differently from all of them) is the cause of 
this correspondence of their phenomena, and causes what is private 
to one to be public to all ; otherwise there would be no connection. 



LEIBNIZ'S ETHICS. 291 

G. IV. 533. In order that an action should be not miraculous, 
it is not sufficient that it should conform to a general law. For if 
this law were not founded in the nature of things, perpetual miracles 
would be required to execute it.... Thus it is not enough that God 
should order the body to obey the soul, and the soul to have 
perception of what happens in the body; he must give them a 
means of doing so, and I have explained this means. 

G. VII. 390 (D. 255). God, being moved by his supreme 
reason to choose, among many possible series of things or worlds, 
that in which free creatures should take such or such resolutions, 
though not without his concourse, has thereby rendered every 
event certain and determined once for all ; without derogating 
thereby from the liberty of those creatures : that simple decree of 
choice not at all changing, but only actualizing, their free natures, 
which he saw in his ideas. 

G. VII. 358 (D. 242). If God is obliged to mend the course 
of nature from time to time, it must be done either supernaturally 
or naturally. If it be done supernaturally, we must have recourse 
to miracles to explain natural things, which is reducing an hypo- 
thesis ad ahsurdum ; for everything may easily be accounted for by 
miracles. But if it be done naturally, then God wUl not be 
intelligentia swpramundana : he wiU be comprehended under the 
nature of things ; that is, he will be the soul of the world. 

XV. § 117. Ood's goodness. 

G. VII. 399 (D. 264). I have still other reasons against this 
strange imagination, that space is a property of God. If it be so, 
space belongs to the essence of God. But space has parts : therefore 
there would be parts in the essence of God. Spectatum admissi. 

G. VII. 416 (D. 281). The immensity and eternity of God 
would subsist, though there were no creatures ; but those attributes 
would have no dependence either upon times or places.... These 
attributes signify only that God would be present and coexistent 
with all the things that should exist. 

r 

XVI. § 118. Freedom and determinism. 

G. VI. 29. There are two famous labyrinths, where our reason 
very often goes astray ; one is concerned with the great question 
of the free and the necessary, especially in the production and origin 
of evil. 

19—2 



292 LEIBNIZ'S ETHICS. 

G. VI. 411. If the will determines itself without there being 
anything, either in the person choosing, or in the object chosen, 
which can lead to the choice, there will be neither cause nor reason 
in this election : and as moral evil consists in bad choice, this is to 
admit that moral e-sdl has no source at all. Thus by the rules of 
good metaphysics, there should be no moral evil in nature; and 
also, by the same reason, there would be no moral good either, and 
all morality would be destroyed. 

G. VI. 380 (D. 197). The necessity which is contrary to 
morality, which ought to be avoided, and would make punishment 
unjust, is an insurmountable necessity, which would make all 
opposition useless, even if we wished with all our hearts to avoid 
the necessary action, and though we made all possible efforts to this 
end. Now it is evident that this is not applicable to voluntary 
actions ; since we should not do them unless we wished it. Also 
their prevision and predetermination is not absolute, but presupposes 
the will : if it is certain we shall do them, it is no less certain that 
we shall wish to do them. 

G. II. 419. I should not say that in Adam, or in any one 
else, there was a moral necessity of sinning, but only this : that the 
inclination to sin prevailed in him, and that thus there was a 
certain predetermination, but no necessity. I recognize that there 
is a moral necessity in God to do the best, and in confirmed spirits 
to act well. And in general I prefer to interpret the words thus, 
lest anything should follow which would sound bad. 

G. V. 163 (N. E. 182). It seems to me that, properly speaking, 
though volitions are contingent, necessity should not be opposed to 
volition, but to contingency... and that necessity must not be 
confounded with determination, for there is no less connection or 
determination in thoughts than in motions.... And not only con- 
tingent truths are not necessary, but also their connections are not 
always of an absolute necessity... ; physical things even have some- 
thing moral and voluntary in relation to God, since the laws of 
motion have no other necessity than that of the best. 

G. V. 165 (N. E. 184). [The advocates of free will] demand 
(at least several do so) the absurd and the impossible, in desiring a 
liberty of equilibrium, which is absolutely imaginary and impracti- 
cable, and would not even serve their purpose if it were possible 
for them to have it, i.e. that they should have liberty to will against 
all the impressions which may come from the understanding, which 
would destroy true liberty, and reason also. 



LEIBNIZ'S ETHICS. 293 

G. V. 167 (S. E. 187). We do not will to will, but we will 
to do ; and if we willed to will, we should will to will to will, and 
this would go to infinity. 

G. IV. 362 (D. 54). To ask whether there is freedom in our 
will, is the same as asking whether there is will in our will. Free 
and voluntary mean the same thing. 

G. VII. 419 (D. 285). AH the natural powers of spirits are 
subject to moral laws. 

G. VI. 130. The reason which M. Des Cartes has alleged, for 
proving the independence of our free actions by a pretended lively 
internal feeling, has no force. We cannot properly feel our inde- 
pendence, and we do not always perceive the often imperceptible 
causes upon which our resolution depends. 

G. VI. 421. Not only free creatures are active, but also all 
other substances, and natures composed of substances. Beasts are 
not free, and yet they do not fail to have active souls. 

G. I. 331 (1679). Whatever acts, is free in so far as it acts. 

G. VI. 122. There is contingency in a thousand actions of 
nature ; but when there is no judgment in the agent, there is no 
liberty. 



XVI. § 119. Psychology of volition and pleasure. 

G. V. 149 (N. E. 167). Ph. The Good is what is proper to 
produce and increase pleasure in us, or to diminish and abridge 
some pain. Hvil is proper to produce or increase pain in us, or 
to diminish some pleasure. Th. I am also of this opinion. 

G. V. 171 (N. E. 190). I would not have it believed... that 
we must abandon those ancient axioms, that the will follows the 
greatest good, or flies the greatest evil, which it feels. The source 
of the little application to the truly good comes, in great part, from 
the fact that, in the affairs and occasions where the senses scarcely 
act, most of our thoughts are surd {sov/rdes), so to speak,... i.e. void 
of perception and feeling, and consisting in the bare employment of 
' symbols.... Now such knowledge cannot move us; we need something 
lively {vif) in order to feel emotion. 

G. V. 173 (N. E. 193). We must, once for all, make this law 
for ourselves : henceforth to await and to follow the conclusions of 
reason, once understood, though only perceived in the sequel usually 
by surd thoughts, and destitute of sensible attractions. 

G. V. 175 (N. B. 194). Uneasiness is essential to the felicity 



294 Leibniz's ethics. 

of creatures, which never consists in complete possession, which 
would make them insensible and stupid, but in a continual and un- 
interrupted progress to greater goods. 

G. VII. 73 (D. 130). Pleasure or delight is a sense of per- 
fection, i.e. a sense of something which helps or assists some power. 

G. V. 179 (N. E. 200). In tlie moment of combat, there is no 
longer time to use artifices ; all that then strikes us weighs in the 
balance, and helps to form a compound direction, almost as in 
Mechanics. 

G. VI. 385 (D. 202). [In answer to the proposition that he 
who cannot fail to choose the best is not free :] It is rather true 
liberty, and the most perfect, to be able to use one's free will in the 
best way, and always to iise this power without being turned aside 
either by external force or by internal passions. 

G. V. 179 (N. E. 201). I do not know whether the greatest 
pleasure is possible; I should rather think that it can grow 
infinitely. 

G. V. 180 (N. E. 201). Although pleasure cannot receive a 
nominal definition, any more than light or colour, yet it can, like 
them, receive a causal definition, and I believe that, at bottom, 
pleasure is a feeling of perfection and pain a feeling of imperfection, 
provided they are sufiicieutly remarkable for us to be able to 
perceive them. 

G. VI. 266. Properly speaking, perception is not enough to 
cause misery, if it is not accompanied by reflection. The same is 

true of felicity We cannot reasonably doubt that there is pain in 

animals ; but it seems that their pleasures and pains are not as 
lively as in man, they are not susceptible either of the sorrow 
(chagrin) which accompanies pain, or of the joy which accompanies 
pleasure. 



XVI. § 120. Sin. 

G. IV. 300 (D. 9) (ca. 1680). Immortality without memory 
is quite useless to morals ; for it destroys all reward and all 
punishment. 

G. VI. 118. Moral evil is so great an evil as it is only because 
it is a source of physical evils. 

G. VI. 141. There is a kind of justice, and a certain sort of 
rewards and punishments, which appears inapplicable to those who 
act from an absolute necessity, if there were any such. This is the 



Leibniz's ethics. 295 

kind of justice which has not for its object amendment, or example, 
or even the reparation of evil. This justice is founded only in 
fitness, which demands a certain satisfaction as the expiation of a 
bad action. 

G. IV. 454 (1686). It depends upon the soul to guard against 
the surprises of appearances by a firm will to make reflections, and 
neither to act nor to judge, in certain circumstances, without great 
and mature deliberation. 

G. VII. 92. Virtue is an unchangeable precept of the mind, 
and a perpetual renewing of the same, by which we are as it were 
driven to perform what we believe to be good. ... Since our will is 
not drawn to obtain or avoid anything, except as the understanding 
presents it to the will as something good or bad, it will suffice that 
we should always judge rightly, in order to our always acting 
rightly. 

G. VII. 99. The chief rule of our life is, that we should always, 
as far as possible, exactly do or leave undone what not the passions, 
but the understanding, shows to be the most useful or the most 
harmful ; and that when we have done this, we should then, however 
it turns out, account ourselves happy. 



XVI. § 121. Meaning of good and evil ; three kinds of each. 

G. VII. 74 (D. 130). The perfection of the universe, or 
harmony of things, does not allow all minds to be equally perfect. 
The question why God has given to one mind more perfection than 
to another is among senseless questions. 

G. VI. 376 (D. 194). It must be admitted that there is evil 
in this world which God has made, and that it was possible to 
make a world without evil, or even to create no world at all ... ; but 
. . .the better part is not always that which tends to avoid evil, since 
it may be that the evil is accompanied by a greater good. 

G, IV. 427 (1686). We must know what a perfection is, and 
here is a sufficiently certain mark of one : forms or natures which 
are not capable of the last degree, are not perfections, as for 
example the nature of number or figure. For the greatest of all 
numbers (or the number of all numbers), as well as the greatest 
of all figures, imply a contradiction; but the greatest knowledge 
and omnipotence do not involve impossibility. 

G. VII. 303 (D. 101 ; L. 340). Perfection is nothing but 
quantity of essence. 



296 Leibniz's ethics. 

G. III. 33. The ultimate origin of evil must not be sought in 
the divine will, but in the original imperfection of creatures, which 
is contained ideally in the eternal truths constituting the internal 
object of the divine intellect, so that evil could not be excluded from 
the best possible system of things. 

G. VII. 194 (ca. 1677?). Absolutely first truths are, among 
truths of reason, those which are identical, and among truths of 
fact this, from which all experiments can be proved ct priori, 
namely : Everything possible demands that it should exist, and hence 
will exist unless something else prevents it, which also demands 
that it should exist and is incompatible with the former ; and hence 
it follows that that combination of things always exists by which 
tihe greatest possible number of things exists ; as, if we assume 
A, B, 0, D to be equal as regards essence, i.e. equally perfect, or 
equally demanding existence, and if we assume that D is incom- 
patible with A and with £, while A is compatible with any except 
D, and similarly as regards £ and C ; it follows that the combina- 
tion ABC, excluding D, will exist; for if we wish D to exist, it 
can only coexist with C, and hence the combination CD will exist, 
which is more imperfect than the combination ABC. And hence 
it is obvious that things exist in the most perfect way. This 
proposition, that everything possible demands that it should exist, 
can be proved d, posteriori, assuming that something exists ; for 
either all things exist, and then every possible so demands existence 
that it actually exists ; or some things do not exist, and then a 
reason must be given why some things exist rather than others. 
But this cannot be given . otherwise than from a general reason of 
essence or possibility, assuming that the possible demands existence 
in its own nature, and indeed in proportion to its possibility or 
according to the degree of its essence. Unless in the very nature of 
Essence there were some inclination to exist, nothing would exist ; for 
to say that some essences have this inclination and others not, is 
to say something without a reason*, since existence seems to be 
referred generally to every essence in the same way. But it is as 
yet unknown to men, whence arises the incompossibility of diverse 
things, or how it can happen that diverse essences are opposed to 

* Leibniz remarks in the margin: If existence were anything other than 
what is demanded by essence {essentiae exigentia), it would follow that it itself 
would have a certain essence, or would add something new to things, concerning 
which it might again be asked, whether this essence exists, and why this rather 
than another. 



Leibniz's ethics. 297 

each other, seeing that all purely positive terms seem to be com- 
patible inter se. 

G. VII. 195 {ca. 1677?). The Good is what contributes to 
perfection. But perfection is what involves the most of essence. 



XVI. § 122. Metaphysical evil the source of the other 
two kinds. 

Gr. VI. 162. Grod concurs in moral and physical evil, and in 
both in a moral and in a physical manner; man also concurs 
morally and physically in a free and active way, which renders him 
blameworthy and punishable. 

Gr. VI. 237. It might be said that the whole series of things 
to infinity may be the best that is possible, although what exists 
throughout the universe in each part of time is not the best. It 
would be possible, therefore, for the universe to go always from 
better to better, if the nature of things were such that it is not 
permitted to attain the best all at once. But these are problems 
concerning which it is difficult for us to judge. 

Gr. VI. 378 (D. 196). God is infinite, and the Devil is limited; 
the good can and does go to infinity, whereas evil has its bounds. 

G. II. 317. Vice is not a potentiality of acting, but a hindrance 
to the potentiality of acting. 



XVI. § 123. Connection with tlie doctrine of analytic 
judgments. 

G. V. 242 (N. E. 272). If any one wished to write as a 
mathematician in Metaphysics and Morals, nothing would hinder 
him from doing so with rigour. 

G. V. 18 (D. 98 ; N. E. 17). I strongly approve of Mr. Locke's 
doctrine concerning the demonstrability of moral truths. 

G. II. 578 (D. 128). The felicity of God does not compose a 
part of our happiness, but the whole. 

G. II. 581 (D. 129). To love truly and disinterestedly is 
nothing else than to be led to find pleasure in the perfections or the 
felicity of the object.... This love has properly for its object, sub- 
stances capable of felicity. 



298 LEIBNIZ'S ETHICS. 

XVI. § 124. The kingdoms of nature and of grace. 

G. IV. 480 (D. 73 ; L. 304). Spirits have special laws which 
put them above the revolutions of matter through the very order 
which God has placed there ; and it may be said tliat everything else 
is made only for them, these revolutions themselves being arranged 
for the felicity of the good and the punishment of the wicked. 

G. VI. 168. I agree that the happiness of intelligent creatures 
is the principal part of God's designs, for they most resemble him ; 
but I do not see how it can be proved that this is his sole aim. It 
is true that the kingdom of nature must be helpful to the kingdom 
of grace ; but as everything is connected in God's great design, we 
must believe that the kingdom of grace is also in some way fitted 
to the kingdom of nature, in such a manner that this keeps the 
greatest order and beauty, so as to render the whole composed of 
both the most perfect possible. 

Gr. IV. 462 (1686). Felicity is to persons what perfection is to 
beings. And if the first principle of the existence of the physical 
world is the decree giving it as much perfection as possible, the 
first design of the moral world or City of God, which is the noblest 
part of the universe, must be to distribute through it the greatest 
possible felicity. 

G. IV. 391 (D. 63). Nature has, as it were, an empire within 
an empire, and so to speak a double kingdom, of reason and of 
necessity, or of forms and of particles of matter. 

G. VI. 621 (D. 231 J L. 266). Among other differences which 
exist between ordinary souls and minds [esjB«<«]... there is also this : 
that souls in general are living mirrors or images of the universe 
of created things, but that minds are also images of the Deity or 
Author of nature himself, capable of knowing the system of the 
universe, and to some extent of imitating it.... It is this that enables 
minds to enter into a kind of fellowship with God, and brings it 
about that in relation to them he is not only what an inventor is 
to his machine (which is the relation of God to other created things) 
but also what a prince is to his subjects, and even what a father is 
to his children. Whence it is easy to conclude that the totality 
of all minds must compose the City of God, i.e. the most perfect 
State that is possible, under the most perfect of Monarchs. This 
City of God, this truly universal monarchy, is a moral world in the 
natural world, and is the most exalted and the most divine among 
the works of God ; and it is in it that the glory of God really 



LEIBNIZ'S ETHICS. 299 

consists, for he would have no glory were not his greatness and his 
goodness known and admired by minds. It is also in relation to 
this divine City that God properly has goodness, while his wisdom 
and his power are manifested everywhere. As we have shown 
above that there is a perfect harmony between the two realms in 
nature, the one of efficient, the other of final causes, we should here 
notice also another harmony, between the physical realm of nature 
and the moral realm of grace, i.e. between God considered as Architect 
of the machine of the universe and God considered as Monarch of 
the divine City of Spirits. A result of this harmony is that things 
lead' to grace by the very ways of nature, and that this globe, for 
instance, must be destroyed and renewed by natural means at the 
very time when the government of spirits requires it, for the 
punishment of some and the reward of others. It may also be 
said that God as Architect satisfies in all respects God as Lawgiver, 
and thus that sins must bear their penalty with them, through the 
order of nature, and even in virtue of the mechanical structure 
of things ; and similarly that noble actions will attain their rewards 
by ways which, in relation to bodies, are mechanical, although this 
cannot and ought not always to happen immediately. 

Ifote to § 105. Many quotations relative to this subject (some 
from unpublished MS.) are given by Peano, " Formules de Logique 
Math^matique,'' Revue de Mathemattques, T. vii. No. 1. 



INDEX TO APPENDIX. 



G. I. 



G. II. 



Page 


Paragraph 


52 


69 


54 


69 


57 


105 


58 


37 


331 


118 


838 


58 


352 


102 


372 


19, 33 


382 


79 


388 


75 


384 


11 


403 


45, 58 


416 


60 


12 


17, 77 


13 


84 


37 


17 


39 


18 


40 


13, 14 


43 


17 


45 


17 


46 


8 


49 


15. 


54 


17 


56 


15 


68 


54, 79, 90 


68 


79 


71 


37, 75 


74 


75 


75 


91 


76 


17 


77 


17, 57, 91 


91 


41 


92 


49 


96 


55 


97 


55 


98 


57 



G. II. 



Page 


Paragraph 


100 


90 


112 


68 


115 


41 


116 


48 


118 


91 


119 


77 


120 


91 


121 


99 


125 


113 


131 


23 


135 


54 


136 


77, 79 


137 


41 


168 


27 


169 


18, 37 


170 


38 


171 


88 


181 


15 


182 


27 


183 


72 


193 


27 


226 


79 


233 


10, 37, 50 


240 


10 


248 


87 


249 


16, 23 


250 


10 


251 


91 


252 


85 


253 


71 


256 


75 


258 


22 


261 


52, 68 


262 


49 


263 


19 


264 


18 


265 


103 



302 



INDEX TO APPENDIX. 



G. II. 



Page 
267 
268 
269 
271 
275 
277 
278 
279 
282 
300 
304 
305 
306 
315 
317 
324 
325 
339 
347 
356 
368 
370 
371 
378 
379 
399 
407 
412 
419 
423 
424 
435 
436 
438 
444 
450 
457 
458 
460 
461 
475 
481 
486 
503 
510 
515 
516 
517 



Paragraph 
55 
55 
54 

17, 67 
55 

67, 71 
59 

60 

69 

60 

60, 63, 91 

58, 68 

86, 90 

58 

75, 122 

87 

86 

71 

67 

90 

86, 91 
55, 71, 91 
91 

71, 90 
59 

47, 92 
47 

87, 102 
49, 118 
15 

15 
92 
71 

68, 71 
71 

71 

17 

17 

87 

92 

46, 59 

92 

10 

77 

53 

60 

33, 86, 92 

63, 92 





Page 


Paragraph 


G. II. 


520 


92 




578 


123 




581 


123 


G. III. 


33 


121 




45 


42 




48 


42 




52 


27 




54 


13 




60 


39 




69 


55 




97 


37 




143 


79 




144 


79 




216 


105 




247 


17 




356 


90 




363 


90 




400 


11, 13, 31 




443 


11 




453 


37 




457 


49 




479 


99 




565 


94 




572 


107 




573 


29 




575 


75 




580 


47 




581 


72 




582 


26 




583 


59 




591 


60 




622 


88 




623 


49, 71 




636 


49, 86 




645 


13 




657 


35, 91 




659 


99 


&. IV. 


286 


36 




3U0 


120 




344 


15 




357 


11, 99 




359 


109. 




360 


109 




362 


118 




364 


17 




368 


46 



INDEX TO APPENDIX. 



303 



G. IV. 



G. V. 



Page 


Paragraph 


369 


41 


391 


91, 124 


393 


38 


394 


52, 53, 59 


395 


38, 46 


396 


39, 49 


400 


.41 


406 


107 


424 


104 


426 


lis 


427 


121 


432 


17 


436 


102 


437 


13 


438 


14 


440 


77, 114 


441 


84 


450 


104 


454 


120 


462 


124 


469 


17, 18 


470 


39 


478 


55 


479 


18, 83 


480 


124 


482 


70 


484 


70, 77 


486 


41, 84 


491 


59 


495 


77 


497 


36 


507 


18 


SOS 


18 


509 


18 


510 


89 


511 


91 


512 


70 


513 


39 


523 


42 


533 


49, 114 


574 


71 


582 


22 


15 


99 


18 


123 


21 


11 


24 


68 


46 


18 



G. V. 



Pane 


Paragraph 




48 


96 




49 


27, 96 




52 


46 




66 


99 




70 


99 




71 


99 




76 


99 




77 


102 




79 


96, 99 




92 


11 




94 


53 




96 


17 




97 


96 




100 


18, 23, 66, 


99 


101 


75 




107 


96 




108 


102 




109 


96 




115 


52, 67 




117 


102 




129 


10 




137 


17 




139 


72, 99 




140 


67 




142 


59, 67 




144 


58 




145 


58 




148 


96 




149 


119 




156 


99 




158 


43 




163 


118 




165 


118 




167 


118 




171 


119 




173 


119 




175 


119 




179 


119 




180 


119 




196 


49 




197 


102 




200 


18 




201 


84 




202 


25 




205 


33, 71 




206 


38 




209 


58 




210 


10 





304 



INDEX TO APPENDIX. 



G. V. 



G. VI. 



Page 


Paragraph 


Page 


Paragraph 


213 


23 ( 


Gr. VI. 123 


13 


214 


90 


130 


118 


-218 


83 


141 


120 " 


219 


83 


152 


94 


220 


102 


162 


122 


242 


123 


167 


114 


243 


103 


168 


124 


248 


104 


226 


111 


268 


26 


230 


113 


274 


17, 104 


237 


122 


275 


33, 104 


266 


119 


279 


99 


319 


13 


284 


83 


323 


11 


286 


29 


327 


75 


290 


83 


350 


17 


300 


104 


352 


94 


309 


91 


376 


121 


324 


99 


378 


122 


325 


38 


380 


118 


338 


99 


385 


119 


340 


99 


405 


74 


342 


11 


411 


118 


343 


11 


421 


118 


347 


11, 99 


423 


113 


355 


33 


493 


17 


359 


54 


499 


102 


363 


102 


500 


102 


370 


41 


502 


102 


373 


102 


505 


99 


377 


10 


539 


90 


378 


10 


540 


36 


391 


99 


543 


90, 94 


415 


99 


546 


87 


417 


109 


576 


75 


419 


107 


577 


75 


420 


107 


581 


16 


421 


114 


582 


16 


428 


13 


585 


16, 52 


455 


27 


595 


90 


460 


lOS 


598 


51, 71, 90 


461 


105 


599 


75 


472 


103 


600 


83 


473 


27 


604 


83 






607 


77 


29 


118 


608 


68, 75 


107 


114 


609 


75 


118 


120 


610 


83 


122 


118 


612 


11 



INDEX TO APPENDIX. 



305 



G. VI. 



G. VII. 



Page 


Paragraph 








Page 


Paragraph 


614 


106 


G, 


, VII. 


399 


52, 117 


615 


84 








400 


67 


619 


90 








402 


72 


621 


124 








408 


41 


629 


58 








404 
407 


60 
23 


20 


105 








408 


72 


73 


119 








410 


75 


74 


121 








415 


72, 117 


92 


120 








419 


' 15, 118 


99 


120 








468 


90 


185 


105 








501 


35 


190 


111 








502 


91 


194 


121 








529 


83 


195 


121 








530 


90 


198 


105 








531 


94 


199 


14 








552 


62 


200 


26 












261 


108 


G. 


M. 


II. 


104 


105 


263 


99 








186 


45 


802 


106 








145 


45 


303 


121 








156 


45 


305 


42 








157 


45 


309 


14, 26 








184 


41 


310 


111 












311 


79 


G. 


M. 


IV. 


91 


58 


320 


33 








92 


58 


322 


86 








93 


58 


328 


38 












329 


74 


G. 


M. 


VI. 


230 


43 


355 


11 








235 


39 


356 


46 








237 


89 


358 


114 








238 


49 


363 


66 








247 


41 


364 


15 








251 


43 


365 


114 








252 


42, 43 


372 


23, 46, 66 












373 


72 


G. 


M. 


VII, 


, 18 


60 


374 


14 












375 


74 


F. 


de C. 


24 


26 


377 


46 








28 


53 


389 


31 








62 


75 


390 


114 








70 


114 


393 


23 












396 


46 













K. h. 



20 



INDEX. 



Abstraction is falsification, 110 

Action, at a distance, 91, 93, 236: 
and reaction, 80, 85, 234 

Activity, definition of, 11, 45 : neces- 
sary to substance, 44, 49 m, 215, 
217, 230: and passivity, 46, 189, 
142, 266 : and time, 11, 51 

Aggregates semi-meutal, 13, 115, 116, 
248 

Algebra, Universal, 170 

Animals, 141 

Animal spirits, 140 

Anselm, 172 

Antitypia, 78, 226, 228, 229 

Apperception, 141, 155, 156, 264, 276 

Appetition, belongs to all Monads, 
131, 259, 261: defined, 133, 260 

A priori, not synonymous with neces- 
sary, 23 

Aristotle, influence on Leibniz, 6, 104, 
241 

Arithmetic, analytic or synthetic ? 19, 
21, 24, 207 

Amauld, 6, 7, 8, 44 k, 213 

Ars Combinatoria, 283 

Atoms, and impact, 90, 235 : Leibniz's 
reasons against, 92, 103, 234, 241: 
of substance, 104, 254 

Attributes, 212 

Axioms, 167, 169, 206 

Berkeley, 70, 72, 166 

Body, of Christ, 151 : demands unities, 
103 : different senses of, 75 : mathe- 
matical, 106, 243: organic, 76, 126, 
140, 147, 269 ff. 



Boscovioh, 91 
Boyle, 6 

Bradley, 50 re, 60, 177 
Bruno, 187 

Calculus, infinitesimal, 6, 233 
Cartesiauism, influence on Leibniz, 6, 

123: and substance, 40: and theory 

of impact, 64 
Causality, necessary, 38 : and sufficient 

reason, 30, 36 
Causal laws, as constituting unity of 

substance, 47 : contingent, 27, 29, 

37 n: final, 38, 210: and mutual 

independence of monads, 48: some 

such laws necessary, 67 : synthetic, 

16 
Causation, autonomy of, 96, 98, 136, 

238 
Causes, equal to effects, 81, 85, 233 : 

final, 4, 34, 133, 143, 191, 201 
Change, continuity of, 83, 127, 245 
Gharacteristica Universalis, 169, 282 
Choice, of God, 35, 37: and sufScient 

reason, 35 
City of God, 141, 201, 298 
Clarke, 112, 119, 138 
Clocks, illustration of, 136 
Cogito, 166, 277 
Compatibility, 18, 20, 174, 287 
Composition, only in concretes, 112 
Compossibility, 20 n, 66, 67, 223 
Compound, presupposes simple, 100, 

103 
Connection, two kinds of, 209 
Constraint, 193 re 



INDEX. 



307 



Contingency, subsists for God, 62: 
not itself contingent, 26: and in- 
finite complexity, 60, 221 

Continuity, of cases, 64, 222: de- 
finition of. 111, 245: of forms, 64, 
169, 223: purely ideal, 111, 245: 
three kinds of, 63, 222 : law of, 63, 
222, 234: and point of view, 65: 
spatio-temporal, 63 

Continuum, 71, 100, 108, 152, 243, 245 

Contradiction, only applies to complex 
ideas, 20, 287 : law of, 22, 166, 207 

Cosmological argument, 175, 288 

Creation, 128, 185, 258 

Death, 155 

Definition, implies complexity, 18, 282 : 
real and nominal, 168, 208, 282 

De Pnncipio Individui, 6 

Des Bosses, 151 

Des Cartes, and simile of clocks, 136 
his cogito, 166 : and Dynamics, 77 
81, 82, 226, 228: and Ethics, 198: 
and existence of external world, 73 
and ontological argument, 172, 286 
and quality of ideas, 167 : and re- 
lation of mind to matter, 81, 139 
and substance, 41 : and theory of 
knowledge, 179 

Determination, is it negation ? 186 

Determinism, and "Dynamics, 81 : 
Leibniz's, 192, 193n 

Dialectic, 110 

Dillmann, ISO 

Dimensions, three necessary, 21, 207 

Discours de Mitaphysique, 3, 7, 8 

Discreteness, defined. 111, 245 

Distance, distinguished from length, 
112, 127 

Dreams, how distinguished from true 
perceptions, 225 

Dynamics, and contingency, 29, 80, 
209 : and Leibniz's metaphysics, 89, 
96, 125, 217 : and relative position, 
121 : subjective theory of, 97 : three 
types of, 90 

Ego, a substance, 4, 42, 215: and 
time, 128, 215 



Elasticity, and atoms, 90 : and im- 
pact, 89, 94 : and monadism, 90 

Empirical, 24 

Entelechy, 104, 129, 144, 150, 217, 
226, 228, 258 

Epistemology, 160 

Erdmann, 2, 147, 154, 188 

Essences, exist in the mind of God, 
178 : and necessity, 26 

Eternal truths, hypothetical, 18, 26, 
177, 208 : do not cause knowledge 
of themselves, 134: proof of God 
from, 177, 288 

Ether, 90 

Ethics, Leibniz's, 191, 291 

Eugene, Prince, In 

Evil, contained in best possible world, 
198, 201, 295 : three kinds of, 197, 
295: a limitation, 189, 201, 297: 
and pain, 298 

Existence, an idea of reflection, 162 : 
a mark of contingency, 26 : a pre- 
dicate, 27, 174, 185 : not a predicate, 
296n: not contained in subject, 9, 
27 

Expression, defined, 132 

Extension, presupposes materia prima, 
145 : phenomenal, 108 : means re- 
petition, 102, 240: distinguished 
from space, 101, 289 : prior to space? 
126 : presupposes substances, 102 : 
not unanalyzable, 228 

Felicity, 195, 298 

Fischer, Kuno, 147 

Fluid, all-pervading, 89, 90: motion 
of, 98 b, 94 

Force, centres of, 91 : conservation of, 
280, 234, 288: and continuity of 
motion, 87, 230, 233: derivative, 
79, 95, 237 : and doctrine of monads, 
87 : as entelechy, 95, 281, 237, 242 : 
p rior to extension . 81, 229 : and 
impact, 89,233,237: and independ- 
ence of substances, 81, 94, 97, 98: 
and individuality, 94: required by 
inertia, 88, 230 : and Leibniz's 
philosophy, 80 : measure of, 77, 81 : 
passive, 78, 229, 231 : primitive, 79, 



308 



INDEX. 



95, 237: its reality, 107, 232, 233: 
and relativity of motion, 84, 86, 
281 

Form, as force, 95, 133, 230: sul)- 
stantial, 150, 151, 153n, 242, 269 

Fractions, not sums of parts. 111, 
246 

Freedom, and contingency, 69, 192, 
211, 292: defined, 191: and deter- 
minism, 191, 291 : and final causes, 
149 

Gassendi, 6, 70, 91 

Genus and species, 17 

Geometry, 21, 206, 283 

Gerhardt, Iji, 2 

Geulincx, 81, 136 

God, his goodness necessary? 39, 177 : 

his goodness proved, 189 : called a 

monad, 187 : has no point of view, 

146: possibility of, 19, 173, 287: 

proofs of, 123, 172, 284 
Good, and existence, 34 i three kinds 

of, 197: and pleasure, 193, 293: 

and Beality, 201 
Gravitation, rejected by Leibniz, 89, 

91, 236 

Hegel, 109, 110, 188 
Hobbes, 6, 21, 70, 195 k, 208 
Huygens, 6, 85, 91, 92 

Ideas, defined, 278: innate, 161, 165, 
276 : need not resemble their ob- 
jects, 133 : possible, 19 : quality of, 
167, 281 : of sense, 161, 166 : simple, 
18 

Identity, moral, 141 

Immortality, 141, 265, 294 

Impact, 79, 89, 91, 94 

Impenetrability, 78, 146, 231 

Incessability, 141, 265 

Inconsistencies, two kinds in Leibniz, 
3 : in his premisses, 117 : due to 
theology, 188 

Indifference of equilibrium, 156, 193, 
292 

Indiscernible substances inconceivable, 
57 



Indisoernibles, identity of, stated, 54, 
219 : proved, 55, 57, 219 : and 
plurality of substances, 58 : and ex- 
tension, 103 : and space and time, 
56, 119 
Individual, involves contingency, 26 : 
and infinity, 61 : relation to species, 
62 
Indivisibles, two kinds of, 111 
Inertia, 78, 80, 83, 146, 228, 230, 238 
Infinite, actual,-109, 129m, 243: aggre- 
gate not a whole, 109, 244 : number, 
109n, 110, 244 : true, 109, 244 
Influxus physicus, 137 
Instants, not parts of time, 111, 114, 

120, 247, 257 
Instincts, innate, 195, 206 
Intellect, intimate to itself, 162 

Justice, vindictive, 294 

Kant, his a pi-iori, 23, 157, 163 : and 
centres of force, 91 : and forms of 
intuition, 102 : and measure of 
force, 77 : and theory of knowledge, 
162, 163 : and ontological argument, 
26, 174, 188 : and perception, 138 f 
and theory of relations, 14: and 
absolute space, 119 : and subjec- 
tivity of space, 74, 99 : and syn- 
thetic propositions, 16, 22 : and 
things in themselves, 15, 133 

Kepler, 228, 229 

Knowledge, clear and obscure, 167 : 
distinct and confused, 168: ade- 
quate and inadequate, 168 : sym- 
bolical and intuitive, 168 : innate, 
134 : not caused by what is known, 
134 : theory of, 160 

Latta, 100 

Limitation, internal, 145 

Line, not composed of parts, 112 

Locke, 93 n, 147, 155, 160, 194, 288 

Logic, symbolic, 170 

Lotze, 67 w, 91, 118, 135, 138 

Machine, organic, 144, 148, 269 
Malebranphe, 6, 41, 137, 184, 212 



INDEX. 



809 



78, 79, 243: discrete but in- 
finitely divided, 108, 245 

Materia prima defined, 76, 78, 79, 
228, 268 : distinct from extension, 
80, 229: extended, 102: and pas- 
sivity, 139, 144, 226, 267: and sin, 
196, 198 

Materia secunda, 76, 80, 144, 226, 229, 
240 

Materialism, 70, 71, 128 

Matter, a datum for Leibniz, 70: its 
essence not extension, 77, 140, 227 : 
its existence, 72: its constituents 
not material, 105,248: metaphysical, 
145 : cannot act on mind, 135 : 
different senses of, 75, 226 : and 
ideality of space, 74 : appearance of 
substances, 107 

Maxwell, 83 

Memory, 141 

Mind (see Spirits) : consists in a point, 
123, 253 

Miracle, only one required by Leibniz, 
137, 264, 291: in generation, 154, 
274 

Momentum, 81, 226, 227 
: Monad, defined, 100, 226 : dominant, 

140, 141, 147, 254 : and materia 
prima, 144, 267 : mirrors the uni- 
verse, 131, 137, 262: has position, 
125 : how related to space, 122, 129, 
252 

Monadism, and the continuum, 71, 
108 : and God, 172, 185 : and inde- 
pendence of substances, 136 : and 
space, 118, 122, 126 : and time, 128 

Monads, bare, 141 : three classes of, 

141, 264: mutually independent, 
134, 135, 262 : common qualities 
of, 131 : distinguished by internal 
qualities, 131 

Monadology, In, S 

Monas Monadum, 187 

Morals, demonstrable, 297 

Motion, and continuity, 82, 87, 127: 
and force, 83 : phenomenal, 238 : 
and point of view, 155 : relativity 
of, 84: and relativity of position, 



Nature and Grace, 201, 298: Prin- 
ciples of, 1 

Necessity, meaning of, 23 : three kinds 
of, 69, 223, 292 

New Essays, 134, 161 

Newton, 6 n, 85, 91, 112, 119, 232 

Number, relational, 14, 116 : infinite, 
109 m, 110 

Occasionalism, 81, 132, 136, 140 
One, prior to fractious. 111, 246: only 

number which is a predicate, 115 
Ontological argument, 172, 286 

Pantheism, in Leibniz, 183, 186 

Passion, spontaneous, 95, 145 : and 
pain, 195 

Passivity, 46, 139, 140, i44n, 192 

Pearson, Karl, 123 

Perception, defined, 116, 130, 259, 
261 : distinct and confused, 140, 
144, 146, 155 : infinitely complex, 
147, 157 : minute, 157 : belongs to 
all monads, 131, 259, 261: not 
caused by object, 132, 133, 164, 225, 
260, 261: and simultaneity, 130: 
its trustworthiness a premiss for 
Leibniz, 4, 75, 131, 225 : uncon- 
scious, 147, 156, 275, 276 

Perfection, and clearness of perception, 
141, 143, 266: defined, 174, 189, 
200, 287, 295 : and existence, 34, 
73, 189, 198, 296: and pleasure, 
194, 294 

Phenomena, always divisible, 106 

Place, defined, 121, 252: and point 
of view, 113 

Plato, 5, 7, 197 m 

Pleasure and Pain, 142, 194, 201«, 
267, 293 

Plenum, motion in, 93 ra, 97, 129, 235 

Points, mathematical, 103, 104, 113, 
114, 123, 241, 254: metaphysical, 
104, 124, 241, 254: physical, 105, 
123, 148, 153, 254: not parts of 
space. 111, 114, 120: of view, 113, 
122, 124, 146, 155, 186, 254 

Possible, requires possible cause, 26, 
36 n (see Worlds) 



310 



INDEX. 



Predicaments, 162, 277 

Predicate (see Subject) 

Predicates, contingent, 10, 28, 29 

Pre-established harmony, and Dy- 
namics, 81 : and perception, 133, 
136,263: proof of God from, 183, 290 

Pre-formation, 154, 274 

Premisses, Leibniz's, 4 

Presence, kinds of, 124, 290: in a 
volume, 125, 158 

Propositions, analysis of, 8 : analytic, 
4, 10, 16, 22 : dichotomy of, 30 : 
existential, 25, 29, 177, 182 : iden- 
tical, 19 : necessary and contingent, 
4, 9, 16, 33, 197 K, 207, 208: syn- 
thetic, 10, 16, 21 

Psychical disposition, 157, 164, 166 

Psychology, 160 

Quantity, infinite, 115 ; intensive and 
extensive, 114 : applies to orders, 
114 m, 248 

Batio, 12, 111, 114k, 248 

Beason (see Sufficient) : inclining, 32, 

38, 176 : belongs to spirits, 141 
Eelations, merely ideal? 13, 14, 130: 

two kinds of, 206 
Besistance, 78, 228, 229, 240 

Scholasticism, 6 

Self-consciousness, 141, 162 

Sensation, 135, 143, 158 

Series, causal, 48, 97, 98, 135 

Simultaneity, 52, 130 

Sin, 196, 292, 294 

Situation, defined, 120 

Solipsism, reasons against, 70, 224 

Soul and Body, 187, 139, 147, 205, 
269 ff. 

Souls, each a world apart, 10, 43, 205 : 
defined, 141, 265: in points? 122, 
124, 253 ft. : always think, 155 

Space, not an absolute being, 118, 
249 : not an attribute, 119, 249 : 
its existence contingent, 130, 259: 
three kinds of, 130: and Leibniz's 
logic, 118 : its relation to monads, 
122, 252 ff.. relational theory of. 



113, 251 : relational theory essential 
to Monadism, 119: subjective? 122, 
126, 129 : not a substance, 119 : 
two theories of, 112 : same in all 
possible worlds, 126, 129 Y • ^"^^ 

Species, involves only necessary truths, 
26, 209 ' 

Spinoza, and activity, 44 n, 94 n: and 
geometricfal method, 170 : influence 
on Leibniz, 5, 6, 139, 287: and 
limitation, 145 : and metaphysical 
perfection, 197n : and monism, 126, 
179 : and relation of mind to matter, 
81, 136, 140 : and pleasure-pain, 
195 n: and substance, 41: and suf- 
ficient reason, 33 n 

Spirits, defined, 141, 264: ends in 
themselves, 148, 201, 298: never 
disembodied, 147 

Spontaneity, 198 

Statics, 81 

Stein, 136 n, 154n 

Subject, and predicate, every propo- 
sition contains, 4, 9, 12: contains 
predicate, 9, 17, 33, 205, 210, 214, 
216: defined by its predicates? 28, 
48, 49, 59, 220 

Substance, corporeal, 77, 106, 144, 
151, 226 : definition of, 4, 10, 42, 
212, 213, 239: objections to 126; 
has infinite number of predicates, 
60, 213, 221 : must be analogous to 
soul, 105 : involves all its states, 
10, 48, 138, 213 : and time, 42, 50, 
217, 219 : unextended, 105, 227 

Sufficient Beason, 10, 27, 31, 32, 209: 
actual and possible distinguished, 
36, 143 n : two principles of, 80, 35, 
86 : relation to law of contradiction, 
35, 86, 211 

Syllogism, 170, 282 

Tabula rasa, 158 

Thgodicee, 1, 22 

Time, not a real being, 50, 120, 129, 
250, 257 : and contingency, 25, 29 : 
distinguished from duration, 239: 
its existence contingent, 30 : three 
kinds of, 130: past, logically prior 



INDEX. 



311 



to future, 128, 257 : a plenum, 127, 
138, 258 : its properties necessary, 
30, 129 : relational theory of, 120, 
127, 250, 258 : consists of relations 
of predicates, 128 : and substance, 
50 ___ jr 
Transubstantiation, 78 n, 151 
Truths, of fact, 166, 207 : innate, 157, 
161, 276 : of reason, 166, 207 : their 
relation to knowledge, 181, 289 

Ubiety, 124, 255 

Uneasiness, 194, 293 

Unity, necessary to reality, 108, 150, 

289, 241, 242 
Unumperse, 150, 226, 271 

Vacuum, and atoms, 98: proof of, 77n, 

227 : reasons against, 73, 92, 235 
Van Helmont, 188n 



Vinculum mibstantiaU, 151, 273 
Virtue, 196, 295 
Vis Viva, 81, 82, 96, 237 
Volition, law of, 29, 37, 133, 143, 196, 
259, 261, 293 

Weismann, 154 

Whole, only applicable to indivisible, 

115 : prior to parts in ideals. 111, 

112, 245 : subsequent to parts in 

actuals. 111, 245 
Wolff, 58n, 140« 
World, external, its existence only 

probable, 72, 74, 167, 224: Imown 

confusedly, 162 
Worlds, possible, correspond to possible 

designs of God, 36, 210 : described, 

68 
Wundt, 81 



CantbriDse: 

PKINTED BY J. AND 0. F. OIiAY, 
AT THE UNIVEBSinr PRESS. 



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